Detecting the presence of a tumor based on methylation status of cell-free nucleic acid molecules

Abstract

In implementations described herein, methylation information is determined with respect to classification regions of a reference genome that are related to the presence of a tumor in a subject. The methylation information can be analyzed using a number of computational techniques to provide metrics related to the presence or absence of a tumor in a given subject. In one or more examples, the methylation information can be analyzed using one or more computational models that generate output corresponding to an indication of a tumor being present in a subject. The one or more computational models can be trained using training data selected from a subset of available training data according to one or more criteria.

Description

DETECTING THE PRESENCE OF A TUMOR BASED ON METHYLATION STATUS OF CELL-FREE NUCLEIC ACID MOLECULESCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of priority of US Provisional Application No. 63 / 583,748 filed September 19, 2023 and US Provisional Application No. 63 / 588,679 filed October 6, 2023, each of which is incorporated by reference herein in its entirety for all purposes.BACKGROUND

[0002] Cancer is a major cause of disease worldwide. Each year, tens of millions of people are diagnosed with cancer around the world, and more than half eventually die from it. In many countries, cancer ranks the second most common cause of death following cardiovascular diseases. Early detection is associated with improved outcomes for many cancers.

[0003] Cancer can be caused by the accumulation of genetics variations within an individual's normal cells, at least some of which result in improperly regulated cell division. Such variations commonly include copy number variations (CNVs), single nucleotide variations (SNVs), gene fusions, insertions and / or deletions (indels), epigenetic variations including 5-methylation of cytosine (5-methylcytosine) and association of DNA with chromatin and transcription factors.

[0004] Cancers are often detected by biopsies of tumors followed by analysis of cells, markers or DNA extracted from cells. But more recently it has been proposed that cancers can also be detected from cell-free nucleic acids in body fluids, such as blood or urine. Such tests have the advantage that they are noninvasive and can be performed without identifying suspected cancer cells in biopsy. However, such tests are complicated by the fact that the amount of nucleic acids in body fluids is very low and what nucleic acids are present are heterogeneous in form (e.g., RNA and DNA, single-stranded and double- stranded, and various states of post-replication modification and association with proteins, such as histones).

[0005] Thus, there is a need for improved systems and methods for improved cancer detection using liquid biopsy assays. Therefore, it is an object of the disclosure to providecomputer-implemented systems and methods that have improved capability to classify a sample as containing tumor-derived DNA with heightened sensitivity.BRIEF DESCRIPTION OF THE DRAWINGS

[0006] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate certain implementations, and together with the written description, serve to explain certain principles of the methods, computer readable media, and systems disclosed herein. The description provided herein is better understood when read in conjunction with the accompanying drawings which are included by way of example and not by way of limitation. It will be understood that like reference numerals identify like components throughout the drawings, unless the context indicates otherwise. It will also be understood that some or all of the figures may be schematic representations for purposes of illustration and do not necessarily depict the actual relative sizes or locations of the elements shown.

[0007] Figure 1 is a diagrammatic representation of an example environment 100 that identifies nucleic acids that correspond to classification regions of a reference sequence, where the classification regions have at least a threshold number of CpGs.

[0008] Figure 2 is a diagrammatic representation of an example architecture to determine tumor metrics based on one or more models that analyze methylation status of cell free nucleic acid molecules, according to one or more implementations.

[0009] Figure 3 is a diagrammatic representation of an example architecture to train one or more machine learning models to determine cancer metrics based on methylation status of cell-free nucleic acid molecules, according to one or more implementations.

[0010] Figure 4 is a diagrammatic representation of a framework for generating training data for use in training a computational model that determines indications of cancer being present in subjects, in accordance with one or more example implementations.

[0011] Figure 5 is a diagrammatic representation of a framework of a training process for a computational model that produces indications of cancer being present in one or more subjects, in accordance with one or more example implementations.

[0012] Figure 6 is a diagrammatic framework of a process to train a computational model using biological sample data and in silico training data, in accordance with one or more example implementations.

[0013] Figure 7 is a flow diagram of an example process to determine tumor metrics related to levels of methylation of classification regions of a reference sequence, according to one or more implementations.

[0014] Figure 8 is a flowchart of an example method to train a computational model that generates one or more indications of tumors being present in one or more subjects, according to one or more implementations.

[0015] Figure 9 is a block diagram illustrating components of a machine, in the form of a computer system, that may read and execute instructions from one or more machine- readable media to perform any one or more methodologies described herein, in accordance with one or more example implementations.

[0016] Figure 10 is block diagram illustrating a representative software architecture that may be used in conjunction with one or more hardware architectures described herein, in accordance with one or more example implementations.

[0017] Figure 11 shows the limits of detection in relation to the tumor fraction for the first version of a regression model and the second version of the regression model.

[0018] Figure 12 shows the sensitivity for three models in relation to specificity. The bottom line shows results from a first model that does not implement regression model techniques described herein. The middle line shows results from a second model that corresponds to the first version of the regression model and the top line shows results from a third model that corresponds to the second version of the regression model.Figure 13 shows the limits of detection in relation to the tumor fraction for the first version of the model and the second version of the model with respect to the detection of lung cancer and breast cancer.SUMMARY

[0019] In one or more aspects, a method includes obtaining training sequence data including training sequencing reads derived from a plurality of samples of a first plurality of subjects, where a tumor is detected in the first plurality of subjects, determining, using a first computational model and based on the first training sequence data, individual values of a quantitative measure for individual samples of the plurality of samples, the individual values of the quantitative measure indicating an amount of mutant allelespresent in first nucleic acids of the individual samples, analyzing the individual values of the quantitative measure to determine a subset of the plurality of samples having respective values of the quantitative measure within a specified range of values, determining a first group of training samples from the subset of the plurality of samples having nucleic acids with one or more somatic mutations present, obtaining a second group of training samples derived from a second plurality of subjects, where a tumor is not detected with respect to the second plurality of subjects, performing a training process for a second computational model using training data derived from the first group of training samples and the second group of training samples to produce a trained version of the second computational model, analyzing, using the second computational model, test sequencing reads derived from one or more samples of one or more test subjects to determine an indication of cancer being present in the one or more test subjects.

[0020] In one or more aspects, a method includes analyzing, using a second computational model, test sequencing reads derived from one or more samples of one or more test subjects to determine an indication of cancer being present in the one or more test subjects with a specificity of at least 90%, wherein the second computational model is trained by obtaining training sequencing reads derived from a plurality of samples obtained from a plurality of first subjects in which a tumor is detected; determining, using a first computational model and based on the training sequencing reads, individual values of a quantitative measure for individual samples of the plurality of samples, the individual values of the quantitative measure indicating an amount of mutant alleles present in first nucleic acids of the individual samples; analyzing the individual values of the quantitative measure to determine a subset of the plurality of samples having respective values of the quantitative measure within a specified range of values; and determining a first group of training samples from the subset of the plurality of samples having nucleic acids with one or more somatic mutations present, wherein the training data for the second computational model includes the first group of training samples and a second group of training samples obtained from additional subjects in which a tumor is not detected. In one or more aspects of the methods, the training process for the second computational model includes a first iteration that includes determining first training data corresponding to the first group of training samples and including the respective values of the quantitativemeasure within the specified range of values, determining second training data including one or more pseudo values for the quantitative measure for the second group of training samples, and determining an initial version of the second computational model based on the first training data and the second training data.

[0021] In one or more aspects, the methods may also include analyzing the subset of the plurality of samples to determine a third group of training samples in which somatic mutations are absent, and determining, using the initial version of the second computational model and based on additional training sequences derived from the third group of training samples, additional individual values of the quantitative measure that correspond to individual training samples of the third group of training samples.

[0022] In one or more aspects, the method may also include obtaining third training data that includes at least a portion of the additional individual values of the quantitative measure that correspond to the individual training samples of the third group of training samples. In one or more aspects of the method, the training process for the second computational model includes a second iteration that includes determining a subsequent version of the second computational model based on the first training data, the second training data, and the third training data.

[0023] In one or more aspects, the methods may also include determining, based on further training sequences derived from the second group of training samples, further individual values of the quantitative measure, determining a threshold value for the quantitative measure that corresponds to at least a threshold number of the second group of training samples, determining that one or more third samples have respective additional individual values of the quantitative measure that are less than the threshold value, and modifying the respective additional individual values of the quantitative measure to correspond to the threshold value in the third training data.

[0024] In one or more aspects, the methods may also include determining, for the training process of the second computational model, first weights for the plurality of samples of the first plurality of subjects, where the first weights are based on a first number of the plurality of samples, and determining, forthe training process of the second computational model, second weights for the second group of training samples derived from the secondplurality of subjects, where the second weights are based on a second number of the second group of training samples and an additional weighting factor.

[0025] In one or more aspects of the methods, the second computational model is trained using a loss function.

[0026] In one or more aspects of the methods, the loss function includes a Huber loss function, a support vector regression loss function, a ridge loss function, a lasso loss function, an elastic net loss function, or a square error loss function.

[0027] In one or more aspects of the methods, the second computational model is included in a plurality of computational models that determine indications of cancer being present in individuals, and the method includes determining a plurality of groupings of the training data, where individual groupings of the plurality of groupings of the training data include a training portion and a validation portion, and performing training processes for the plurality of computational models using the plurality of groupings of the training data.

[0028] In one or more aspects, the methods may also include analyzing the individual values of the quantitative measures to determine an additional subset of the plurality of samples having additional respective values of the quantitative measure outside of the specified range of values, identifying one or more first samples from among the additional subset of the plurality of samples, and identifying one or more second samples from among an additional plurality of samples, the additional plurality of samples being obtained from subjects in which a tumor is not detected.

[0029] In one or more aspects of the methods, a plurality of types of cancer are detected in the first plurality of subjects, and the second computational model determines a plurality of indications of cancer being present in the one or more test subjects, individual indications of cancer being present in the one or more test subjects corresponding to an individual type of cancer of the plurality of types of cancer.

[0030] In one or more aspects of the methods, a single type of cancer is detected in the first plurality of subjects and the indication of cancer being present in the one or more test subjects corresponds to the single type of cancer.

[0031] In one or more aspects of the methods, the indication of cancer being present in the one or more test subjects includes a first result indicating a tumor being detected ora second result indicating a tumor not being detected with respect to individual test subjects of the one or more test subjects.

[0032] In one or more aspects of the methods, the indication of cancer being present in the one or more test subjects includes a numerical value on a scale with the numerical value corresponding to at least one of a stage of cancer present in individual test subjects of the one or more test subjects, a probability of cancer being present in individual test subjects of the one or more test subjects, an estimate of tumor fraction for the individual test subjects of the one or more test subjects, or a progression of cancer present in individual test subjects of the one or more test subjects.

[0033] In one or more aspects of the methods, individual training sequencing reads include a nucleotide sequence corresponding to a fragment of a nucleic acid included in a sample of the plurality of samples, and the method includes analyzing the training sequencing reads to determine a first region quantitative measure derived from the training sequencing reads that corresponds to individual classification regions of a plurality of classification regions, at least a portion of the individual classification regions of the plurality of classification regions corresponding to genomic regions of a reference genome that have the threshold amount of methylated cytosines in subjects in which cancer is detected and that have at least the threshold cytosine-guanine content, analyzing the training sequencing reads to determine a second region quantitative measure derived from the training sequencing reads that correspond to a plurality of control regions, individual control regions of the plurality of control regions corresponding to additional genomic regions of the reference genome that have at least the threshold cytosine-guanine content and that have at least the threshold amount of methylated cytosines in subjects in which cancer is detected and in additional subjects in which cancer is not detected, and determining a metric for the individual classification regions of the plurality of classification regions based on the first region quantitative measure for the individual classification regions and the second region quantitative measure for the plurality of control regions.

[0034] In one or more aspects of the methods, individual training sequencing reads correspond to molecules have a threshold amount of methylated cytosines included in regions of the nucleotide sequence having at least a threshold cytosine-guanine content.

[0035] In one or more aspects of the methods, the training process for the second computational model includes; performing a plurality of training processes for a plurality of instances of the second computational model using the training data, determining, based on individual training processes of the plurality of training processes, at least one of weights of variables or values of parameters for individual instances of the second computational model, and combining the at least one of weights of variable or values of parameter for the individual instances of the second computational model to determine an aggregate model that corresponds to the second computational model.

[0036] In one or more aspects of the methods, the second computational model comprises a linear regression model.

[0037] In one or more aspects of the methods, the indication of cancer being present in the one or more test subjects is a numerical value, and the method comprises: analyzing the indication of cancer being present in the one or more test subjects with respect to a threshold value; and determining that cancer is present in a test subject of the one or more test subjects in response to determining that the indication of cancer being present is at least the threshold value.

[0038] In one or more aspects of the methods, the threshold value includes a tumor fraction or a probability of a type of cancer being present in the test subject.

[0039] In one or more aspects of the methods, the threshold value corresponds to a minimum specificity of at least 90% with respect to the second computational model.

[0040] In one or more aspects, a computing apparatus includes a processor. The computing apparatus also includes a memory storing instructions that, when executed by the processor, configure the computing apparatus to obtain training sequence data including training sequencing reads derived from a plurality of samples of a first plurality of subjects, where a tumor is detected in the first plurality of subjects, determine, using a first computational model and based on the first training sequence data, individual values of a quantitative measure for individual samples of the plurality of samples, the individual values of the quantitative measure indicating an amount of mutant alleles present in first nucleic acids of the individual samples, analyze the individual values of the quantitative measure to determine a subset of the plurality of samples having respective values of the quantitative measure within a specified range of values, determine a first group of trainingsamples from the subset of the plurality of samples having nucleic acids with one or more somatic mutations present, obtain a second group of training samples derived from a second plurality of subjects, where a tumor is not detected with respect to the second plurality of subjects, perform a training process for a second computational model using training data derived from the first group of training samples and the second group of training samples to produce a trained version of the second computational model, analyze, using the second computational model, test sequencing reads derived from one or more samples of one or more test subjects to determine an indication of cancer being present in the one or more test subjects.

[0041] In one or more aspects, a computing apparatus includes a processor. The computing apparatus also includes a memory storing instructions that, when executed by the processor, configure the computing apparatus to analyze, using a second computational model, test sequencing reads derived from one or more samples of one or more test subjects to determine an indication of cancer being present in the one or more test subjects with a specificity of at least 90%, wherein the second computational model is trained by obtaining training sequencing reads derived from a plurality of samples obtained from a plurality of first subjects in which a tumor is detected; determining, using a first computational model and based on the training sequencing reads, individual values of a quantitative measure for individual samples of the plurality of samples, the individual values of the quantitative measure indicating an amount of mutant alleles present in first nucleic acids of the individual samples; analyzing the individual values of the quantitative measure to determine a subset of the plurality of samples having respective values of the quantitative measure within a specified range of values; and determining a first group of training samples from the subset of the plurality of samples having nucleic acids with one or more somatic mutations present, wherein the training data for the second computational model includes the first group of training samples and a second group of training samples obtained from additional subjects in which a tumor is not detected.

[0042] In one or more aspects of the computing apparatuses, the memory stores additional instructions that, when executed by the processor, configure the apparatus to analyze the subset of the plurality of samples to determine a third group of training samples in which somatic mutations are absent, and determine, using the initial versionof the second computational model and based on additional training sequences derived from the third group of training samples, additional individual values of the quantitative measure that correspond to individual training samples of the third group of training samples.

[0043] In one or more aspects of the computing apparatuses, the memory stores additional instructions that, when executed by the processor, configure the apparatus to obtain third training data that includes at least a portion of the additional individual values of the quantitative measure that correspond to the individual training samples of the third group of training samples.

[0044] In one or more aspects of the computing apparatuses, the training process for the second computational model includes a second iteration that includes determining a subsequent version of the second computational model based on the first training data, the second training data, and the third training data.

[0045] In one or more aspects of the computing apparatuses, the memory stores additional instructions that, when executed by the processor, configure the apparatus to determine, based on further training sequences derived from the second group of training samples, further individual values of the quantitative measure, determine a threshold value for the quantitative measure that corresponds to at least a threshold number of the second group of training samples, determine that one or more third samples have respective additional individual values of the quantitative measure that are less than the threshold value, and modify the respective additional individual values of the quantitative measure to correspond to the threshold value in the third training data.

[0046] In one or more aspects of the computing apparatuses, the memory stores additional instructions that, when executed by the processor, configure the apparatus to determine, for the training process of the second computational model, first weights for the plurality of samples of the first plurality of subjects, where the first weights are based on a first number of the plurality of samples, and determine, for the training process of the second computational model, second weights for the second group of training samples derived from the second plurality of subjects, where the second weights are based on a second number of the second group of training samples and an additional weighting factor.

[0047] In one or more aspects of the computing apparatuses, the training process for the second computational model includes a first iteration that includes determining first training data corresponding to the first group of training samples and including the respective values of the quantitative measure within the specified range of values, determining second training data including one or more pseudo values for the quantitative measure for the second group of training samples, and determining an initial version of the second computational model based on the first training data and the second training data.

[0048] In one or more aspects of the computing apparatuses, the memory stores additional instructions that, when executed by the processor, configure the apparatus to determine, for the training process of the second computational model, first weights for the plurality of samples of the first plurality of subjects, where the first weights are based on a first number of the plurality of samples, and determine, for the training process of the second computational model, second weights for the second group of training samples derived from the second plurality of subjects, where the second weights are based on a second number of the second group of training samples and an additional weighting factor.

[0049] In one or more aspects of the computing apparatuses, the second computational model is trained using a loss function.

[0050] In one or more aspects of the computing apparatuses, the loss function includes a Huber loss function, a support vector regression loss function, a ridge loss function, a lasso loss function, an elastic net loss function, or a square error loss function.

[0051] In one or more aspects of the computing apparatuses, the second computational model is included in a plurality of computational models that determine indications of cancer being present in individuals, and the memory stores additional instructions that, when executed by the processor, configure the apparatus to determine a plurality of groupings of the training data, where individual groupings of the plurality of groupings of the training data include a training portion and a validation portion, and perform training processes for the plurality of computational models using the plurality of groupings of the training data.

[0052] In one or more aspects of the computing apparatuses, the memory stores additional instructions that, when executed by the processor, configure the apparatus to analyze the individual values of the quantitative measures to determine an additional subset of the plurality of samples having additional respective values of the quantitative measure outside of the specified range of values, identify one or more first samples from among the additional subset of the plurality of samples, and identify one or more second samples from among an additional plurality of samples, the additional plurality of samples being obtained from subjects in which a tumor is not detected.

[0053] In one or more aspects of the computing apparatuses, a plurality of types of cancer are detected in the first plurality of subjects, and the second computational model determines a plurality of indications of cancer being present in the one or more test subjects, individual indications of cancer being present in the one or more test subjects corresponding to an individual type of cancer of the plurality of types of cancer.

[0054] In one or more aspects of the computing apparatuses, a single type of cancer is detected in the first plurality of subjects and the indication of cancer being present in the one or more test subjects corresponds to the single type of cancer.

[0055] In one or more aspects of the computing apparatuses, the indication of cancer being present in the one or more test subjects includes a first result indicate a tumor being detected or a second result indicating a tumor not being detected with respect to individual test subjects of the one or more test subjects.

[0056] In one or more aspects of the computing apparatuses, the indication of cancer being present in the one or more test subjects includes a numerical value on a scale with the numerical value corresponding to at least one of a stage of cancer present in individual test subjects of the one or more test subjects, a probability of cancer being present in individual test subjects of the one or more test subjects, an estimate of tumor fraction for the individual test subjects of the one or more test subjects, or a progression of cancer present in individual test subjects of the one or more test subjects.

[0057] In one or more aspects of the computing apparatuses, individual training sequencing reads include a nucleotide sequence corresponding to a fragment of a nucleic acid included in a sample of the plurality of samples, and the memory stores additional instructions that, when executed by the processor, configure the apparatus to analyze thetraining sequencing reads to determine a first region quantitative measure derived from the training sequencing reads that corresponds to individual classification regions of a plurality of classification regions, at least a portion of the individual classification regions of the plurality of classification regions corresponding to genomic regions of a reference genome that have the threshold amount of methylated cytosines in subjects in which cancer is detected and that have at least the threshold cytosine-guanine content, analyze the training sequencing reads to determine a second region quantitative measure derived from the training sequencing reads that correspond to a plurality of control regions, individual control regions of the plurality of control regions corresponding to additional genomic regions of the reference genome that have at least the threshold cytosine- guanine content and that have at least the threshold amount of methylated cytosines in subjects in which cancer is detected and in additional subjects in which cancer is not detected, and determine a metric for the individual classification regions of the plurality of classification regions based on the first region quantitative measure for the individual classification regions and the second region quantitative measure for the plurality of control regions.

[0058] In one or more aspects of the computing apparatuses, individual training sequencing reads correspond to molecules have a threshold amount of methylated cytosines included in regions of the nucleotide sequence having at least a threshold cytosine-guanine content.

[0059] In one or more aspects of the computing apparatuses, the second computational model comprises a linear regression model.

[0060] In one or more aspects of the computing apparatuses, the indication of cancer being present in the one or more test subjects is a numerical value, and the method comprises: analyzing the indication of cancer being present in the one or more test subjects with respect to a threshold value; and determining that cancer is present in a test subject of the one or more test subjects in response to determining that the indication of cancer being present is at least the threshold value.

[0061] In one or more aspects of the computing apparatuses, the threshold value includes a tumor fraction or a probability of a type of cancer being present in the test subject.

[0062] In one or more aspects of the computing apparatuses, the threshold value corresponds to a minimum specificity of at least 90% with respect to the second computational model.

[0063] In one or more aspects of the computing apparatuses, the training process for the second computational model includes: performing a plurality of training processes for a plurality of instances of the second computational model using the training data, determining, based on individual training processes of the plurality of training processes, at least one of weights of variables or values of parameters for individual instances of the second computational model, and combining the at least one of weights of variable or values of parameter for the individual instances of the second computational model to determine an aggregate model that corresponds to the second computational model.

[0064] In one or more aspects, a non-transitory computer-readable storage medium, the computer-readable storage medium including instructions that when executed by a computer, cause the computer to obtain training sequence data including training sequencing reads derived from a plurality of samples of a first plurality of subjects, where a tumor is detected in the first plurality of subjects, determine, using a first computational model and based on the first training sequence data, individual values of a quantitative measure for individual samples of the plurality of samples, the individual values of the quantitative measure indicating an amount of mutant alleles present in first nucleic acids of the individual samples, analyze the individual values of the quantitative measure to determine a subset of the plurality of samples having respective values of the quantitative measure within a specified range of values, determine a first group of training samples from the subset of the plurality of samples having nucleic acids with one or more somatic mutations present, obtain a second group of training samples derived from a second plurality of subjects, where a tumor is not detected with respect to the second plurality of subjects, perform a training process for a second computational model using training data derived from the first group of training samples and the second group of training samples to produce a trained version of the second computational model, analyze, using the second computational model, test sequencing reads derived from one or more samples of one or more test subjects to determine an indication of cancer being present in the one or more test subjects.

[0065] In one or more aspects, a non-transitory computer-readable storage medium, the computer-readable storage medium including instructions that when executed by a computer, cause the computer to analyze, using a second computational model, test sequencing reads derived from one or more samples of one or more test subjects to determine an indication of cancer being present in the one or more test subjects with a specificity of at least 90%, wherein the second computational model is trained by obtaining training sequencing reads derived from a plurality of samples obtained from a plurality of first subjects in which a tumor is detected; determining, using a first computational model and based on the training sequencing reads, individual values of a quantitative measure for individual samples of the plurality of samples, the individual values of the quantitative measure indicating an amount of mutant alleles present in first nucleic acids of the individual samples; analyzing the individual values of the quantitative measure to determine a subset of the plurality of samples having respective values of the quantitative measure within a specified range of values; and determining a first group of training samples from the subset of the plurality of samples having nucleic acids with one or more somatic mutations present, wherein the training data for the second computational model includes the first group of training samples and a second group of training samples obtained from additional subjects in which a tumor is not detected.

[0066] In one or more aspects of the non-transitory computer-readable storage media, the training process for the second computational model includes a first iteration that includes determining first training data corresponding to the first group of training samples and including the respective values of the quantitative measure within the specified range of values, determining second training data including one or more pseudo values for the quantitative measure for the second group of training samples, and determining an initial version of the second computational model based on the first training data and the second training data.

[0067] In one or more aspects, the non-transitory computer-readable storage media store additional instructions that when executed by a computer, cause the computer to analyze the subset of the plurality of samples to determine a third group of training samples in which somatic mutations are absent, and determine, using the initial version of the second computational model and based on additional training sequences derived from the thirdgroup of training samples, additional individual values of the quantitative measure that correspond to individual training samples of the third group of training samples.

[0068] In one or more aspects, the non-transitory computer-readable storage media store additional instructions that when executed by a computer, cause the computer to obtain third training data that includes at least a portion of the additional individual values of the quantitative measure that correspond to the individual training samples of the third group of training samples.

[0069] In one or more aspects of the non-transitory computer-readable storage media, the training process for the second computational model includes a second iteration that includes determine a subsequent version of the second computational model based on the first training data, the second training data, and the third training data.

[0070] In one or more aspects, the non-transitory computer-readable storage media store additional instructions that when executed by a computer, cause the computer to determine, based on further training sequences derived from the second group of training samples, further individual values of the quantitative measure, determine a threshold value for the quantitative measure that corresponds to at least a threshold number of the second group of training samples, determine that one or more third samples have respective additional individual values of the quantitative measure that are less than the threshold value, and modify the respective additional individual values of the quantitative measure to correspond to the threshold value in the third training data.

[0071] In one or more aspects of the non-transitory computer-readable storage media, the training process for the second computational model includes a first iteration that includes determining first training data corresponding to the first group of training samples and including the respective values of the quantitative measure within the specified range of values, determining second training data including one or more pseudo values for the quantitative measure for the second group of training samples, and determining an initial version of the second computational model based on the first training data and the second training data.

[0072] In one or more aspects, the non-transitory computer-readable storage media store additional instructions that when executed by a computer, cause the computer to determine, for the training process of the second computational model, first weights forthe plurality of samples of the first plurality of subjects, where the first weights are based on a first number of the plurality of samples, and determine, for the training process of the second computational model, second weights for the second group of training samples derived from the second plurality of subjects, where the second weights are based on a second number of the second group of training samples and an additional weighting factor.

[0073] In one or more aspects of the non-transitory computer-readable storage media, the second computational model is trained using a loss function.

[0074] In one or more aspects of the non-transitory computer-readable storage media, the loss function includes a Huber loss function, a support vector regression loss function, a ridge loss function, a lasso loss function, an elastic net loss function, or a square error loss function.

[0075] In one or more aspects of the non-transitory computer-readable storage media, the second computational model is included in a plurality of computational models that determine indications of cancer being present in individuals, and the non-transitory computer-readable storage medium stores additional instructions that when executed by a computer, cause the computer to determine a plurality of groupings of the training data, where individual groupings of the plurality of groupings of the training data include a training portion and a validation portion, and perform training processes for the plurality of computational models using the plurality of groupings of the training data.

[0076] In one or more aspects, the non-transitory computer-readable storage media store additional instructions that when executed by a computer, cause the computer to analyze the individual values of the quantitative measures to determine an additional subset of the plurality of samples having additional respective values of the quantitative measure outside of the specified range of values, identify one or more first samples from among the additional subset of the plurality of samples, and identify one or more second samples from among an additional plurality of samples, the additional plurality of samples being obtained from subjects in which a tumor is not detected.

[0077] In one or more aspects of the non-transitory computer-readable storage media, a plurality of types of cancer are detected in the first plurality of subjects, and the second computational model determines a plurality of indications of cancer being present in theone or more test subjects, individual indications of cancer being present in the one or more test subjects corresponding to an individual type of cancer of the plurality of types of cancer.

[0078] In one or more aspects of the non-transitory computer-readable storage media, a single type of cancer is detected in the first plurality of subjects and the indication of cancer being present in the one or more test subjects corresponds to the single type of cancer.

[0079] In one or more aspects of the non-transitory computer-readable storage media, the indication of cancer being present in the one or more test subjects includes a first result indicate a tumor being detected or a second result indicating a tumor not being detected with respect to individual test subjects of the one or more test subjects.

[0080] In one or more aspects of the non-transitory computer-readable storage media, the indication of cancer being present in the one or more test subjects includes a numerical value on a scale with the numerical value corresponding to at least one of a stage of cancer present in individual test subjects of the one or more test subjects, a probability of cancer being present in individual test subjects of the one or more test subjects, an estimate of tumor fraction for the individual test subjects of the one or more test subjects, or a progression of cancer present in individual test subjects of the one or more test subjects.

[0081] In one or more aspects of the non-transitory computer-readable storage media, individual training sequencing reads include a nucleotide sequence corresponding to a fragment of a nucleic acid included in a sample of the plurality of samples, and the non- transitory computer-readable storage medium stores additional instructions that when executed by a computer, cause the computer to analyze the training sequencing reads to determine a first region quantitative measure derived from the training sequencing reads that corresponds to individual classification regions of a plurality of classification regions, at least a portion of the individual classification regions of the plurality of classification regions corresponding to genomic regions of a reference genome that have the threshold amount of methylated cytosines in subjects in which cancer is detected and that have at least the threshold cytosine-guanine content, analyze the training sequencing reads to determine a second region quantitative measure derived from the training sequencingreads that correspond to a plurality of control regions, individual control regions of the plurality of control regions corresponding to additional genomic regions of the reference genome that have at least the threshold cytosine-guanine content and that have at least the threshold amount of methylated cytosines in subjects in which cancer is detected and in additional subjects in which cancer is not detected, and determine a metric for the individual classification regions of the plurality of classification regions based on the first region quantitative measure for the individual classification regions and the second region quantitative measure for the plurality of control regions.

[0082] In one or more aspects of the non-transitory computer-readable storage media, individual training sequencing reads correspond to molecules have a threshold amount of methylated cytosines included in regions of the nucleotide sequence having at least a threshold cytosine-guanine content.

[0083] In one or more aspects of the non-transitory computer-readable storage media, the training process for the second computational model includes; performing a plurality of training processes for a plurality of instances of the second computational model using the training data, determining, based on individual training processes of the plurality of training processes, at least one of weights of variables or values of parameters for individual instances of the second computational model, and combining the at least one of weights of variable or values of parameter for the individual instances of the second computational model to determine an aggregate model that corresponds to the second computational model.

[0084] In one or more aspects of the non-transitory computer-readable storage media, the second computational model comprises a linear regression model.

[0085] In one or more aspects of the non-transitory computer-readable storage media, the indication of cancer being present in the one or more test subjects is a numerical value, and the method comprises: analyzing the indication of cancer being present in the one or more test subjects with respect to a threshold value; and determining that cancer is present in a test subject of the one or more test subjects in response to determining that the indication of cancer being present is at least the threshold value.

[0086] In one or more aspects of the non-transitory computer-readable storage media, the threshold value includes a tumor fraction or a probability of a type of cancer being present in the test subject.

[0087] In one or more aspects of the non-transitory computer-readable storage media, the threshold value corresponds to a minimum specificity of at least 90% with respect to the second computational model.

[0088] Other technical features may be readily apparent to one skilled in the art from the following figures, descriptions, and claims.DEFINITIONS

[0089] In order for the present disclosure to be more readily understood, certain terms are first defined below. Additional definitions for the following terms and other terms may be set forth through the specification. If a definition of a term set forth below is inconsistent with a definition in an application or patent that is incorporated by reference, the definition set forth in this application should be used to understand the meaning of the term.

[0090] As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” include plural references unless the context clearly dictates otherwise. Thus, for example, a reference to “a method” includes one or more methods, and / or steps of the type described herein and / or which will become apparent to those persons of ordinary skill in the art upon reading this disclosure and so forth.

[0091] It is also to be understood that the terminology used herein is for the purpose of describing particular implementations only, and is not intended to be limiting. Further, unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure pertains. In describing and claiming the methods, computer readable media, and systems, the following terminology, and grammatical variants thereof, will be used in accordance with the definitions set forth below.[QQS2] About. As used herein, “about” or “approximately” as applied to one or more values or elements of interest, refers to a value or element that is similar to a stated reference value or element. In certain implementations, the term “about” or“approximately” refers to a range of values or elements that falls within 25%, 20%, 19%, 18%, 17%, 16%, 15%, 14%, 13%, 12%, 11%, 10%, 9%, 8%, 7%, 6%, 5%, 4%, 3%, 2%, 1 %, or less in either direction (greater than or less than) of the stated reference value or element unless otherwise stated or otherwise evident from the context (except where such number would exceed 100% of a possible value or element).

[0093] Administer: As used herein, “administer” or “administering” a therapeutic agent (e.g., an immunological therapeutic agent) to a subject means to give, apply or bring the composition into contact with the subject. Administration can be accomplished by any of a number of routes, including, for example, topical, oral, subcutaneous, intramuscular, intraperitoneal, intravenous, intrathecal and intradermal.

[0094] Adapter: As used herein, “adapter” refers to a short nucleic acid (e.g., less than about 500 nucleotides, less than about 100 nucleotides, or less than about 50 nucleotides in length) that can be at least partially double-stranded and used to link to either or both ends of a given sample nucleic acid molecule. Adapters can include nucleic acid primer binding sites to permit amplification of a nucleic acid molecule flanked by adapters at both ends, and / or a sequencing primer binding site, including primer binding sites for sequencing applications, such as various next-generation sequencing (NGS) applications. Adapters can also include binding sites for capture probes, such as an oligonucleotide attached to a flow cell support or the like. Adapters can also include a nucleic acid tag as described herein. Nucleic acid tags can be positioned relative to amplification primer and sequencing primer binding sites, such that a nucleic acid tag is included in amplicons and sequence reads of a given nucleic acid molecule. The same or different adapters can be linked to the respective ends of a nucleic acid molecule. In some implementations, the same adapter is linked to the respective ends of the nucleic acid molecule except that the nucleic acid tag differs. In some implementations, the adapter is a Y-shaped adapter in which one end is blunt ended or tailed as described herein, for joining to a nucleic acid molecule, which is also blunt ended or tailed with one or more complementary nucleotides. In still other example implementations, an adapter is a bell-shaped adapter that includes a blunt or tailed end for joining to a nucleic acid molecule to be analyzed. Other examples of adapters include T-tailed and C-tailed adapters.

[0095] Alignment. As used herein, “alignment” or “align” refers to determining whether at least two sequence representations have at least a threshold amount of homology. In one or more examples, the threshold amount of homology can be at least about 90%, at least about 91%, at least about 92%, at least about 93%, at least about 94%, at least about 95%, at least about 96%, at least about 97%, at least about 98%, at least about 99%, at least about 99.5%, or at least about 99.9%. In situations where two sequence representations have at least the threshold amount of homology, the two sequence representations can be referred to as being “aligned.”

[0096] Amplify: As used herein, “amplify” or “amplification” in the context of nucleic acids refers to the production of multiple copies of a polynucleotide, or a portion of the polynucleotide, starting from a small amount of the polynucleotide (e.g., a single polynucleotide molecule), where the amplification products or amplicons are generally detectable. Amplification of polynucleotides encompasses a variety of chemical and enzymatic processes.

[0097] Barcode: As used herein, “barcode” or “molecular barcode” in the context of nucleic acids refers to a nucleic acid molecule comprising a sequence that can serve as a molecular identifier. For example, individual "barcode" sequences can be added to each DNA fragment during next-generation sequencing (NGS) library preparation so that each read can be identified and sorted before the final data analysis.

[0098] Cancer Type: As used herein, “cancer type” refers to a type or subtype of cancer defined, e.g., by histopathology. Cancer type can be defined by any conventional criterion, such as on the basis of occurrence in a given tissue (e.g., blood cancers, central nervous system (CNS), brain cancers, lung cancers (small cell and non-small cell), skin cancers, nose cancers, throat cancers, liver cancers, bone cancers, lymphomas, pancreatic cancers, bowel cancers, rectal cancers, thyroid cancers, bladder cancers, kidney cancers, mouth cancers, stomach cancers, breast cancers, prostate cancers, ovarian cancers, lung cancers, intestinal cancers, soft tissue cancers, neuroendocrine cancers, gastroesophageal cancers, head and neck cancers, gynecological cancers, colorectal cancers, urothelial cancers, solid state cancers, heterogeneous cancers, homogenous cancers), unknown primary origin and the like, and / or of the same cell lineage (e.g., carcinoma, sarcoma, lymphoma, cholangiocarcinoma, leukemia,mesothelioma, melanoma, or glioblastoma) and / or cancers exhibiting cancer markers, such as Her2, CA15-3, CA19-9, CA-125, CEA, AFP, PSA, HCG, hormone receptor and NMP-22. Cancers can also be classified by stage (e.g., stage 1 , 2, 3, or 4) and whether of primary or secondary origin.

[0099] Carrier Signal: As used herein, “carrier signal” refers to any intangible medium that is capable of storing, encoding, or carrying transitory or non-transitory instructions 902 for execution by the machine 900, and includes digital or analog communications signals or other intangible medium to facilitate communication of such instructions 902. Instructions 902 may be transmitted or received over the network 934 using a transitory or non-transitory transmission medium via a network interface device and using any one of a number of well-known transfer protocols.

[0100] Cell-Free Nucleic Acid: As used herein, “cell-free nucleic acid” refers to nucleic acids not contained within or otherwise bound to a cell or, in some implementations, nucleic acids remaining in a sample following the removal of intact cells. Cell-free nucleic acids can include, for example, all non-encapsulated nucleic acids sourced from a bodily fluid (e.g., blood, plasma, serum, urine, cerebrospinal fluid (CSF), etc.) from a subject. Cell-free nucleic acids include DNA (cfDNA), RNA (cfRNA), and hybrids thereof, including genomic DNA, mitochondrial DNA, circulating DNA, siRNA, miRNA, circulating RNA (cRNA), tRNA, rRNA, small nucleolar RNA (snoRNA), Piwi- interacting RNA (piRNA), long non-coding RNA (long ncRNA), and / or fragments of any of these. Cell-free nucleic acids can be double-stranded, single-stranded, or a hybrid thereof. A cell-free nucleic acid can be released into bodily fluid through secretion or cell death processes, e.g., cellular necrosis, apoptosis, or the like. Some cell-free nucleic acids are released into bodily fluid from cancer cells, e.g., circulating tumor DNA (ctDNA). Others are released from healthy cells. CtDNA can be non-encapsulated tumor-derived fragmented DNA. A cell-free nucleic acid can have one or more epigenetic modifications, for example, a cell-free nucleic acid can be acetylated, 5-methylated, ubiquitylated, phosphorylated, sumoylated, ribosylated, and / or citrullinated.

[0101] Cellular Nucleic Acids: As used herein, “cellular nucleic acids” means nucleic acids that are disposed within one or more cells at least at the point a sample istaken or collected from a subject, even if those nucleic acids are subsequently removed as part of a given analytical process.

[0102] Classification Region: As used herein, “classification region” refers to a genomic region that may show sequence-independent changes in neoplastic cells (e.g., tumor cells and cancer cells) or that may show sequence-independent changes in cfDNA from subjects having cancer relative to cfDNA from subjects in which cancer is not present. Examples of sequence-independent changes include, but are not limited to, changes in methylation rate (increases or decreases), nucleosome distribution, CTCF binding, transcription start sites, and regulatory protein binding regions. In one or more examples, sequence-independent changes in a classification region can indicate the presence of a single form of cancer in a subject. In one or more additional examples, sequence-independent changes in a classification region can correspond to the presence of multiple forms in a subject. The classification region can be enriched by one or more probes. In addition, the classification region can be defined by a pair of primer binding sites. Further, the classification region can be defined by a predetermined beginning genomic locus and a predetermined ending genomic locus. The classification region can include from about 25 nucleotides to about 250 nucleotides, from about 50 nucleotides to about 200 nucleotides, or from about 75 nucleotides to about 150 nucleotides. For instance, classification region can be a differentially methylated region. “Differentially methylated region” or “DMR” refers to a region of DNA having a detectably different degree of methylation in at least one cell or tissue type relative to the degree of methylation in the same region of DNA from at least one other cell or tissue type; or having a detectably different degree of methylation in at least one cell or tissue type obtained from a subject having a disease or disorder relative to the degree of methylation in the same region of DNA in the same cell or tissue type obtained from a healthy subject. In some embodiments, a differentially methylated region has a detectably higher degree of methylation (e.g., a hypermethylated region / hypermethylated target region) in at least one cell or tissue type relative to the degree of methylation in the same region of DNA from at least one other cell or tissue type that contribute to cfDNA in healthy individuals, or from the same cell or tissue type from a healthy subject. In some embodiments, a differentially methylated region has a detectably lower degree of methylation (e.g., a hypomethylatedregion / hypomethylated target region) in at least one cell or tissue type relative to the degree of methylation in the same region of DNA from at least one other cell or tissue type, such as other immune cell types and / or cell types that contribute to cfDNA in healthy individuals, or from the same cell or tissue type from a healthy subject. In some embodiments, the classification regions comprise hypermethylated target regions and / or hypomethylated target regions.

[0103] Communications Network. As used herein, “communications network” refers to one or more portions of a network 114, 1034 that may be an ad hoc network, an intranet, an extranet, a virtual private network (VPN), a local area network (LAN), a wireless LAN (WLAN), a wide area network (WAN), a wireless WAN (WWAN), a metropolitan area network (MAN), the Internet, a portion of the Internet, a portion of the Public Switched Telephone Network (PSTN), a plain old telephone service (POTS) network, a cellular telephone network, a wireless network, a Wi-Fi® network, another type of network, or a combination of two or more such networks. For example, a network 114, 1034 or a portion of a network may include a wireless or cellular network and the coupling may be a Code Division Multiple Access (CDMA) connection, a Global System for Mobile communications (GSM) connection, or other type of cellular or wireless coupling. In this example, the coupling may implement any of a variety of types of data transfer technology, such as Single Carrier Radio Transmission Technology (1xRTT), Evolution- Data Optimized (EVDO) technology, General Packet Radio Service (GPRS) technology, Enhanced Data rates for GSM Evolution (EDGE) technology, third Generation Partnership Project (3GPP) including 3G, fourth generation wireless (4G) networks, Universal Mobile Telecommunications System (UMTS), High Speed Packet Access (HSPA), Worldwide Interoperability for Microwave Access (WiMAX), Long Term Evolution (LTE) standard, others defined by various standard setting organizations, other long range protocols, or other data transfer technology.

[0104] Confidence Interval. As used herein, “confidence interval” means a range of values so defined that there is a specified probability that the value of a given parameter lies within that range of values.

[0105] Control Sample: As used herein, “control sample” or “reference sample” refers to a sample obtained from individuals without known copy number variation.

[0106] Coverage. As used herein, “coverage” or “coverage metrics” refer to the number of nucleic acid molecules or sequencing reads that correspond to a particular genomic region of a reference sequence.

[0107] Deoxyribonucleic Acid or Ribonucleic Acid: As used herein, “deoxyribonucleic acid” or “DNA” refers to a natural or modified nucleotide which has a hydrogen group at the 2'-position of the sugar moiety. DNA can include a chain of nucleotides comprising four types of nucleotide bases: adenine (A), thymine (T), cytosine (C), and guanine (G). As used herein, “ribonucleic acid” or “RNA” refers to a natural or modified nucleotide which has a hydroxyl group at the 2'-position of the sugar moiety. RNA can include a chain of nucleotides comprising four types of nucleotides: A, uracil (U), G, and C. As used herein, the term “nucleotide” refers to a natural nucleotide or a modified nucleotide. Certain pairs of nucleotides specifically bind to one another in a complementary fashion (called complementary base pairing). In DNA, adenine (A) pairs with thymine (T) and cytosine (C) pairs with guanine (G). In RNA, adenine (A) pairs with uracil (U) and cytosine (C) pairs with guanine (G). When a first nucleic acid strand binds to a second nucleic acid strand made up of nucleotides that are complementary to those in the first strand, the two strands bind to form a double strand. As used herein, “nucleic acid sequencing data”, “nucleic acid sequencing information”, “sequence information”, “sequence representation”, “nucleic acid sequence”, “nucleotide sequence”, “genomic sequence”, “genetic sequence”, “fragment sequence”, “sequencing read”, or “nucleic acid sequencing read” denotes any information or data that is indicative of the order and identity of the nucleotide bases (e.g., adenine, guanine, cytosine, and thymine or uracil) in a molecule (e.g., a whole genome, whole transcriptome, exome, oligonucleotide, polynucleotide, or fragment) of a nucleic acid such as DNA or RNA. It should be understood that the present teachings contemplate sequence information obtained using all available varieties of techniques, platforms or technologies, including, but not limited to: capillary electrophoresis, microarrays, ligation-based systems, polymerase-based systems, hybridization-based systems, direct or indirect nucleotide identification systems, pyrosequencing, ion- or pH-based detection systems, and electronic signature-based systems.

[0108] Differentially Methylated Region: As used herein, differentially methylated region” refers to a region of DNA having a detectably different degree of methylation in at least one cell or tissue type relative to the degree of methylation in the same region of DNA from at least one other cell or tissue type; or having a detectably different degree of methylation in at least one ceil or tissue type obtained from a subject having a disease or disorder relative to the degree of methylation in the same region of DNA in the same cell or tissue type obtained from a healthy subject. In some embodiments, a differentially methylated region has a detectably higher degree of methylation (e.g., a hypermethylated region) in at least one cell or tissue type, such as at least one immune cell type, relative to the degree of methylation in the same region of DNA from at least one other cell or tissue type, such as other immune cell types and / or cell types that contribute to cfDNA in healthy individuals, or from the same cell or tissue type from a healthy subject. In some embodiments, a differentially methylated region has a detectably lower degree of methylation (e.g., a hypomethylated region) in at least one cell or tissue type, such as at least one immune cell type, relative to the degree of methylation in the same region of DNA from at least one other cell or tissue type, such as other immune cell types and / or cell types that contribute to cfDNA in healthy individuals, or from the same cell or tissue type from a healthy subject.

[0109] Driver Mutation. As used herein, “driver mutation” means a mutation that drives cancer progression.

[0110] Epigenetic Target Regions. As used herein, “epigenetic target regions” refers to target regions that may show sequence-independent differences in different cell or tissue types (e.g., different types of immune cells) or in neoplastic cells (e.g., tumor cells and cancer ceils) relative to normal cells; or that may show sequence- independent differences (i.e., in which there is no change to the nucleotide sequence, e.g., differences in methylation, nucleosome distribution, or other epigenetic features) in DNA, such as cfDNA, from different cell types or from subjects having cancer relative to DNA, such as cfDNA, from healthy subjects, or in cfDNA originating from different cell or tissue types that ordinarily do not substantially contribute to cfDNA (e.g., immune, lung, colon, etc.) relative to background cfDNA (e.g., cfDNA that originated from hematopoietic ceils). Examples of sequence-independent changes include, but are not limited to, changes inmethylation (increases or decreases), nucleosome distribution, cfDNA fragmentation patterns, CCCTC-binding factor ("CTCF") binding, transcription start sites (e.g., with respect to any one of more of binding of RNA polymerase components, binding of regulatory proteins, fragmentation characteristics, and nucieosomal distribution), and regulatory protein binding regions. Epigenetic target region sets thus include, but are not limited to, hypermethylation target region sets, hypomethylation target region sets, and fragmentation variable target region sets, such as CTCF binding sites and transcription start sites. For present purposes, loci susceptible to neoplasia-, tumor-, or cancer- associated focal amplifications and / or gene fusions may also be included in an epigenetic target region set because detection of a change in copy number by sequencing or a fused sequence that maps to more than one locus in a reference genome tends to be more similar to detection of exemplary epigenetic changes discussed above than detection of nucleotide substitutions, insertions, or deletions, e.g., in that the focal amplifications and / or gene fusions can be detected at a relatively shallow depth of sequencing because their detection does not depend on the accuracy of base calls at one or a few individual positions. An epigenetic target region set is a set of epigenetic target regions.

[0111] Hypermethylation: As used herein, “hypermethylation” refers to an increased level or degree of methylation of nucleic acid molecule(s) relative to the other nucleic acid molecules within a population (e.g., sample) of nucleic acid molecules from the same genomic locus. In some embodiments, hypermethylated DNA can include DNA molecules comprising at least 1 methylated cytosine, at least 2 methylated cytosines, at least 3 methylated cytosines, at least 5 methylated cytosines, or at least 10 methylated cytosines.

[0112] Hypomethylation: As used herein, “hypomethylation” refers to a decreased level or degree of methylation of nucleic acid molecule(s) relative to the other nucleic acid molecules within a population (e.g., sample) of nucleic acid molecules from the same genomic locus. In some embodiments, hypomethylated DNA includes unmethylated DNA molecules. In some embodiments, hypomethylated DNA can include DNA molecules comprising 0 methylated cytosine, at most 1 methylated cytosine, at most 2 methylated cytosines, at most 3 methylated cytosines, at most 4 methylated cytosines, or at most 5 methylated cytosines.

[0113] Immunotherapy. As used herein, “immunotherapy” refers to treatment with one or more agents that act to stimulate the immune system so as to kill or at least to inhibit growth of cancer cells, and preferably to reduce further growth of the cancer, reduce the size of the cancer and / or eliminate the cancer. Some such agents bind to a target present on cancer cells; some bind to a target present on immune cells and not on cancer cells; some bind to a target present on both cancer cells and immune cells. Such agents include, but are not limited to, checkpoint inhibitors and / or antibodies. Checkpoint inhibitors are inhibitors of pathways of the immune system that maintain self-tolerance and modulate the duration and amplitude of physiological immune responses in peripheral tissues to minimize collateral tissue damage (see, e.g., Pardoll, Nature Reviews Cancer 12, 252-264 (2012)). Example agents include antibodies against any of PD-1 , PD-2, PD-L1 , PD-L2, CTLA-40, 0X40, B7.1 , B7He, LAG3, CD137, KIR, CCR5, CD27, or CD40. Other example agents include proinflammatory cytokines, such as IL- 10, IL-6, and TNF-a. Other example agents are T-cells activated against a tumor, such as T-cells activated by expressing a chimeric antigen targeting a tumor antigen recognized by the T-cell.

[0114] Indel: As used herein, “indel” refers to a mutation that involves the insertion or deletion of nucleotides in the genome of a subject.

[0115] Limit of Detection (LoD): As used herein, “limit of detection” means the smallest amount of a substance (e.g., a nucleic acid) in a sample that can be measured by a given assay or analytical approach.

[0116] Machine-Readable Medium: As used herein, “machine-readable medium” refers to a component, device, or other tangible media able to store instructions 902 and data temporarily or permanently and may include, but is not limited to, random-access memory (RAM), read-only memory (ROM), buffer memory, flash memory, optical media, magnetic media, cache memory, other types of storage (e.g., erasable programmable read-only memory (EEPROM)) and / or any suitable combination thereof. The term “machine-readable medium” may be taken to include a single medium or multiple media (e.g., a centralized or distributed database, or associated caches and servers) able to store instructions 902. The term “machine-readable medium” shall also be taken to include any medium, or combination of multiple media, that is capable of storinginstructions 902 (e.g., code) for execution by a machine 900, such that the instructions 902, when executed by one or more processors 904 of the machine 900, cause the machine 900 to perform any one or more of the methodologies described herein. Accordingly, a “machine-readable medium” refers to a single storage apparatus or device, as well as “cloud-based” storage systems or storage networks that include multiple storage apparatus or devices. The term “machine-readable medium” excludes signals per se.

[0117] Maximum MAF. As used herein, “maximum MAF” or “max MAF” refers to the maximum MAF (mutant allele fraction) of all somatic variants in a sample.

[0118] Methylation: As used herein, “methylation” or “DNA methylation” refers to addition of a methyl group to a nucleotide base in a nucleic acid molecule. In some embodiments, methylation refers to addition of a methyl group to a cytosine at a CpG site (cytosine-phosphate-guanine site (i.e., a cytosine followed by a guanine in a 5' 3’ direction of the nucleic acid sequence). In some embodiments, DNA methylation refers to addition of a methyl group to adenine, such as in N6-methyladenine. In some embodiments, DNA methylation is 5-methylation (modification of the 5thcarbon of the 6- carbon ring of cytosine). In some embodiments, 5-methylation refers to addition of a methyl group to the 5C position of the cytosine to create 5-methylcytosine (5mC). In some embodiments, methylation comprises a derivative of 5mC. Derivatives of 5mC include, but are not limited to, 5-hydroxymethylcytosine (5-hmC), 5-formylcytosine (5-fC), and 5- caryboxylcytosine (5-caC). In some embodiments, DNA methylation is 3C methylation (modification of the 3rdcarbon of the 6-carbon ring of cytosine). In some embodiments, 3C methylation comprises addition of a methyl group to the 3C position of the cytosine to generate 3-methylcytosine (3mC). Methylation can also occur at non CpG sites, for example, methylation can occur at a CpA, CpT, or CpC site. DNA methylation can change the activity of methylated DNA region. For example, when DNA in a promoter region is methylated, transcription of the gene may be repressed. DNA methylation is critical for normal development and abnormality in methylation may disrupt epigenetic regulation. The disruption, e.g., repression, in epigenetic regulation may cause diseases, such as cancer. Promoter methylation in DNA may be indicative of cancer.

[0119] Methylation-Dependent Nuclease: As used herein, “methylation- dependent nuclease” refers to a nuclease that preferentially cuts methylated DNA relative to unmethylated DNA. For example, a methylation-dependent nuclease may cut at or near a recognition sequence such as a restriction site in a manner dependent on methylation of at least one of the nucleobases in the recognition sequence, such as a cytosine. In some embodiments, the nucleolytic activity of the methylation-dependent nuclease is at least 10, 20, 50, or 100-fold higher on a methylated recognition site relative to an unmethylated control in a standard nucleolysis assay. Methylation-dependent nucleases include methylation-dependent restriction enzymes.

[0120] Methylation-Dependent Restriction Enzyme: As used herein, “methylation-dependent restriction enzyme” or “MDRE” refers to a restriction enzyme that is dependent on methylation of the DNA (e.g., cytosine methylation) i.e., the presence or absence of methyl group in a nucleotide base alters the rate at which the enzyme cleaves the target DNA. In some embodiments, the methylation dependent restriction enzymes do not cleave the DNA if a particular nucleotide base is unmethylated at the recognition sequence. For example, MspJI is a methylation dependent restriction enzyme with a recognition sequence “mCNNR(N9)” and it does not cleave DNA if the absence of the methylated cytosine (mC) in the recognition sequence.

[0121] Methylation-Sensitive Nuclease: As used herein, “methylation-sensitive nuclease” refers to a nuclease that preferentially cuts unmethylated DNA relative to methylated DNA. For example, a methylation-sensitive nuclease may cut at or near a recognition sequence such as a restriction site in a manner dependent on lack of methylation of at least one of the nucleobases in the recognition sequence, such as a cytosine. In some embodiments, the nucleolytic activity of the methylation-sensitive nuclease is at least 10, 20, 50, or 100-fold higher on an unmethylated recognition site relative to a methylated control in a standard nucleolysis assay. Methylation-sensitive nucleases include methylation- sensitive restriction enzymes.

[0122] Methylation Sensitive Restriction Enzyme: As used herein, “methylation sensitive restriction enzyme” or “MSRE” refers to a restriction enzyme that is sensitive to the methylation status of the DNA (e.g., cytosine methylation) i.e., the presence or absence of methyl group in a nucleotide base alters the rate at which the enzyme cleavesthe target DNA. In some embodiments, the methylation sensitive restriction enzymes do not cleave the DNA if a particular nucleotide base is methylated at the recognition sequence. For example, Hpall is a methylation sensitive restriction enzyme with a recognition sequence “CCGG” and it does not cleave DNA if the second cytosine in the recognition sequence is methylated.

[0123] Methylation rate: As used herein, “methylation rate” refers to the probability, likelihood, or percentage that a given base (for example: cytosine residue in a CpG) is methylated on a DNA molecule at a particular genomic region analyzed in the sample. In some embodiments, the methylation rate may be applied to a defined region that comprises one or more potentially methylated bases. In some embodiments, the methylation rate refers to the percentage of CpG residues methylated in a DNA molecule. In some embodiments, the methylation rate refers to the percentage of CpG residues methylated in molecules aligned to particular genomic position or genomic region. Methylation rate can be measured by a variety of methods including, but not limited to, either using bisulfite sequencing (any single base resolution like TAPS, EM-SEQ, etc.) or using partitioning (DNA molecule resolution). Methylation rate can be measured in different ways. One estimation can be by counting how many DNA fragments end up in each methylation dependent partition or by counting the number of converted CpGs per fragment in the case of bisulfite sequencing or any other base-level resolution sequencing methods. In addition, in the case of methylation dependent partitioning, the rate calculation can be normalized using a set of predefined regions with known methylation state (i.e. , positive control regions and / or negative control regions) or spiked- in synthetic DNA with known methylation state, deriving rate-parametrized partition distributions and estimating the rate using a maximum likelihood approach. In one or more examples, the methylation rate can be determined by determining an abundance of sequencing reads that correspond to a portion of a genomic region. The portion of the genomic region can include a number of genomic locations of the genomic region for which at least a threshold number of sequencing reads overlap.

[0124] Methylation Status: As used herein, “methylation status” or “methylation state” can refer to the presence or absence of methyl group on a DNA base (e.g., cytosine) at a particular genomic position in a nucleic acid molecule. It can also refer tothe degree of methylation in a nucleic acid sequence (e.g., highly methylated, low methylated, intermediately methylated or unmethylated nucleic acid molecules). The methylation status can also refer to the number of nucleotides methylated in a particular nucleic acid molecule.

[0125] Modified Nucleotide Specific Binding Reagent: As used herein, refers to a binding reagent that is specific for, or targets, modified nucleotides. For example, a modified nucleotide can be a nucleotide that has been methylated, thus, the binding reagent can be specific for a methylated nucleotide. Examples of binding reagents include, but are not limited to, a methyl binding domain (MBD) of a methylation binding protein (“MBP”) or variants thereof, an antibody (and antibody variants e.g., single chain antibodies), aptamers, or combinations thereof. Thus, as disclosed throughout, the use of MBD can be exchanged for any other modified nucleotide specific binding reagent, provided the modified nucleotide specific binding reagent has the desired specificity and affinity for the specific modified base of interest in the selected implementation.

[0126] Mutant Allele Fraction. As used herein, “mutant allele fraction”, “mutation dose,” or “MAF” refers to the fraction of nucleic acid molecules harboring an allelic alteration or mutation at a given genomic position in a given sample. MAF is generally expressed as a fraction or a percentage. For example, an MAF can be less than about 0.5, 0.1 , 0.05, or 0.01 (i.e., less than about 50%, 10%, 5%, or 1%) of all somatic variants or alleles present at a given locus.

[0127] Mutation. As used herein, “mutation” refers to a variation from a known reference sequence and includes mutations such as, for example, single nucleotide variants (SNVs), copy number variants or variations (CNVs)Zaberrations, insertions or deletions (indels), gene fusions, transversions, translocations, frame shifts, duplications, repeat expansions, and epigenetic variants. A mutation can be a germline or somatic mutation. In some examples, a reference sequence for purposes of comparison is a wildtype genomic sequence of the species of the subject providing a test sample, typically the human genome.

[0128] Mutation Caller. As used herein, “mutation caller” means an algorithm (embodied in software or otherwise computer implemented) that is used to identify mutations in test sample data (e.g., sequence information obtained from a subject).

[0129] Mutation Count. As used herein, “mutation count” or “mutational count” refers to the number of somatic mutations in a whole genome or exome or targeted regions of a nucleic acid sample.

[0130] Negative Control Region: As used herein, “negative control region”, refers to a genomic region that is expected to be unmethylated or hypomethylated in essentially all samples, regardless of whether the DNA is derived from a cancer cell or a normal cell.

[0131] Neoplasm: As used herein, the terms “neoplasm” and “tumor” are used interchangeably. They refer to abnormal growth of cells in a subject. A neoplasm or tumor can be benign, potentially malignant, or malignant. A malignant tumor is referred to as a cancer or a cancerous tumor.

[0132] Next Generation Sequencing: As used herein, “next generation sequencing” or “NGS” refers to sequencing technologies having increased throughput as compared to traditional Sanger- and capillary electrophoresis-based approaches, for example, with the ability to generate hundreds of thousands of relatively small sequencing reads at a time. Some examples of next generation sequencing techniques include, but are not limited to, sequencing by synthesis, sequencing by ligation, and sequencing by hybridization.

[0133] Nucleic Acid Tag: As used herein, “nucleic acid tag” refers to a short nucleic acid (e.g., less than about 500 nucleotides, about 100 nucleotides, about 50 nucleotides, or about 10 nucleotides in length), used to distinguish nucleic acids from different samples (e.g., representing a sample index), or different nucleic acid molecules in the same sample (e.g., representing a molecular barcode), of different types, or which have undergone different processing. The nucleic acid tag comprises a predetermined, fixed, non-random, random or semi-random oligonucleotide sequence. Such nucleic acid tags may be used to label different nucleic acid molecules or different nucleic acid samples or sub-samples. Nucleic acid tags can be single-stranded, double-stranded, or at least partially double-stranded. Nucleic acid tags optionally have the same length or varied lengths. Nucleic acid tags can also include double-stranded molecules having one or more blunt-ends, include 5’ or 3’ single-stranded regions (e.g., an overhang), and / or include one or more other single-stranded regions at other locations within a given molecule. Nucleic acid tags can be attached to one end or to both ends of the othernucleic acids (e.g., sample nucleic acids to be amplified and / or sequenced). Nucleic acid tags can be decoded to reveal information such as the sample of origin, form, or processing of a given nucleic acid. For example, nucleic acid tags can also be used to enable pooling and / or parallel processing of multiple samples comprising nucleic acids bearing different molecular barcodes and / or sample indexes in which the nucleic acids are subsequently being deconvolved by detecting (e.g., reading) the nucleic acid tags. Nucleic acid tags can also be referred to as identifiers (e.g., molecular identifier, sample identifier). Additionally, or alternatively, nucleic acid tags can be used as molecular identifiers (e.g., to distinguish between different molecules or amplicons of different parent molecules in the same sample or sub-sample). This includes, for example, uniquely tagging different nucleic acid molecules in a given sample, or non-uniquely tagging such molecules. In the case of non-unique tagging applications, a limited number of tags (i.e., molecular barcodes) may be used to tag each nucleic acid molecule such that different molecules can be distinguished based on their endogenous sequence information (for example, start and / or stop positions where they map to a selected reference sequence, a sub-sequence of one or both ends of a sequence, and / or length of a sequence) in combination with at least one molecular barcode. A sufficient number of different molecular barcodes are used such that there is a low probability (e.g., less than about a 10%, less than about a 5%, less than about a 1%, or less than about a 0.1% chance) that any two molecules may have the same endogenous sequence information (e.g., start and / or stop positions, subsequences of one or both ends of a sequence, and / or lengths) and also have the same molecular barcode.

[0134] Partitioning. As used herein, “partitioning” refers to physically separating or fractionating a mixture of nucleic acid molecules in a sample based on a characteristic of the nucleic acid molecules. The partitioning can be physical partitioning of molecules. Partitioning can involve separating the nucleic acid molecules into groups or sets based on the level of epigenetic feature (for e.g., methylation). For example, the nucleic acid molecules can be partitioned based on the level of methylation of the nucleic acid molecules. In some embodiments, the methods and systems used for partitioning may be found in PCT Patent Application No. PCT / US2017 / 068329, which is hereby incorporated by reference in its entirety.

[0135] Partitioned set: As used herein, “partitioned set” or “partition” refers to a set of nucleic acid molecules partitioned into a set or group based on the differential binding affinity of the nucleic acid molecules or proteins associated with the nucleic acid molecules to a binding agent. A partitioned set may also be referred to as a subsample. The binding agent binds preferentially to the nucleic acid molecules comprising nucleotides with epigenetic modification. For example, if the epigenetic modification is methylation, the binding agent can be a methyl binding domain (MBD) protein. In some embodiments, a partitioned set can comprise nucleic acid molecules belonging to a particular level or degree of epigenetic feature (for e.g., methylation). For example, the nucleic acid molecules can be partitioned into three sets - one set for highly methylated nucleic acid molecules (first subsample, hyper partition, hyper partitioned set or hypermethylated partitioned set), a second set for low methylated nucleic acid molecules (second subsample, hypo partition, hypo partitioned set or hypomethylated partitioned set), and a third set for intermediate methylated nucleic acid molecules (third subsample, intermediate partitioned set, intermediately methylated partitioned set, residual partition, or residual partitioned set). In another example, the nucleic acid molecules can be partitioned based on the number of methylated nucleotides - one partitioned set can have nucleic acid molecules with nine methylated nucleotides, and another partitioned set can have unmethylated nucleic acid molecules (zero methylated nucleotides).

[0136] Polynucleotide: As used herein, “polynucleotide”, “nucleic acid”, “nucleic acid molecule”, “polynucleotide molecule”, or “oligonucleotide” refers to a linear polymer of nucleosides (including deoxyribonucleosides, ribonucleosides, or analogs thereof) joined by internucleosidic linkages. A polynucleotide can comprise at least three nucleosides. Oligonucleotides often range in size from a few monomeric units, e.g., 3-4, to hundreds of monomeric units. Whenever a polynucleotide is represented by a sequence of letters, such as “ATGCCTG,” it will be understood that the nucleotides are in 5’ -> 3’ order from left to right and that in the case of DNA, “A” denotes deoxyadenosine, “C” denotes deoxycytidine, “G” denotes deoxyguanosine, and “T” denotes deoxythymidine, unless otherwise noted. The letters A, C, G, and T may be used to refer to the bases themselves, to nucleosides, or to nucleotides comprising the bases, as is standard in the art.

[0137] Positive Control Region. As used herein, As used herein, “positive control region”, refers to a genomic region that is expected to be methylated or hypermethylated in essentially all samples, regardless of whether the DNA is derived from a cancer cell or a normal cell.

[0138] Probe: As used herein, “probe” refers to a polynucleotide comprising a functionality. The functionality can be a detectable label (fluorescent), a binding moiety (biotin), or a solid support (a magnetically attractable particle or a chip). Probes can include single-stranded DNA / RNA polynucleotides or double stranded DNA polynucleotides that hybridize to target nucleic acid sequences (e.g., SureSelect® probes, Agilent Technologies). Sequence capture using probes generally depends, in part, on the number of consecutive nucleotides in at least a portion of the target nucleic acid sequence that is complementary (or nearly complementary) to the sequence of the probe. In some examples, probes can correspond to driver mutations.

[0139] Processing: As used herein, the terms “processing”, “calculating”, and“comparing” can be used interchangeably. In certain applications, the terms refer to determining a difference, e.g., a difference in number or sequence. For example, gene expression, copy number variation (CNV), indel, and / or single nucleotide variant (SNV) values or sequences can be processed.

[0140] Processor: As used herein, “processor” refers to any circuit or virtual circuit (a physical circuit emulated by logic executing on an actual processor) that manipulates data values according to control signals (e.g., “commands,” “op codes,” “machine code,” etc.) and which produces corresponding output signals that are applied to operate a machine. A processor may, for example, be a CPU, a RISC processor, a CISC processor, a GPU, a DSP, an ASIC, a RFIC or any combination thereof. A processor may further be a multi-core processor having two or more independent processors (sometimes referred to as “cores”) that may execute instructions contemporaneously.

[0141] Promoter Region As used herein, “promoter region” refers to a DNA sequence recognized by the synthetic machinery of the cell, or introduced synthetic machinery, required to initiate the specific transcription of a gene.

[0142] Quantitative Measures: As used herein, “quantitative measures” refers to an absolute or relative measure. A quantitative measure can be, without limitation, anumber, a statistical measurement (e.g., frequency, mean, median, standard deviation, or quantile), or a degree or a relative quantity (e.g., high, medium, and low). A quantitative measure can be a ratio of two quantitative measures. A quantitative measure can be a linear combination of quantitative measures. A quantitative measure may be a normalized measure.

[0143] Reference Sequence: As used herein, “reference sequence” refers to a known sequence used for purposes of comparison with experimentally determined sequences. For example, a known sequence can be an entire genome, a chromosome, or any segment thereof. A reference sequence can include at least about 20, at least about 50, at least about 100, at least about 200, at least about 250, at least about 300, at least about 350, at least about 400, at least about 450, at least about 500, at least about 1000, or more nucleotides. A reference sequence can align with a single contiguous sequence of a genome or chromosome or can include non-contiguous segments that align with different regions of a genome or chromosome. Example reference sequences, include, for example, human genome reference sequences, such as, hG19 and hG38.

[0144] Sample: As used herein, “sample” means anything capable of being analyzed by the methods and / or systems disclosed herein.

[0145] Sensitivity: As used herein, “sensitivity” means the probability of detecting the presence of a single nucleotide variant, an insertion, and a deletion at a given MAF and coverage and the probability of detecting the presence of a copy number variant at a given tumor fraction and coverage.

[0146] Sequencing: As used herein, “sequencing” refers to any of a number of technologies used to determine the sequence (e.g., the identity and order of monomer units) of a biomolecule, e.g., a nucleic acid such as DNA or RNA. Example sequencing methods include, but are not limited to, targeted sequencing, single molecule real-time sequencing, exon or exome sequencing, intron sequencing, electron microscopy-based sequencing, panel sequencing, transistor-mediated sequencing, direct sequencing, random shotgun sequencing, Sanger dideoxy termination sequencing, whole-genome sequencing, sequencing by hybridization, pyrosequencing, capillary electrophoresis, duplex sequencing, cycle sequencing, single-base extension sequencing, solid-phase sequencing, high-throughput sequencing, massively parallel signature sequencing,emulsion PCR, co-amplification at lower denaturation temperature-PCR (COLD-PCR), multiplex PCR, sequencing by reversible dye terminator, paired-end sequencing, near- term sequencing, exonuclease sequencing, sequencing by ligation, short-read sequencing, single-molecule sequencing, sequencing-by-synthesis, real-time sequencing, reverse-terminator sequencing, nanopore sequencing, 454 sequencing, Solexa Genome Analyzer sequencing, SOLiD™ sequencing, MS-PET sequencing, and a combination thereof. In some implementations, sequencing can be performer by a gene analyzer such as, for example, gene analyzers commercially available from Illumina, Inc., Pacific Biosciences, Inc., or Applied Biosystems / Thermo Fisher Scientific, among many others.

[0147] Single Nucleotide Variant: As used herein, “single nucleotide variant” or “SNV” means a mutation or variation in a single nucleotide that occurs at a specific position in the genome.

[0148] Somatic Mutation: As used herein, “somatic mutation” means a mutation in the genome that occurs after conception. Somatic mutations can occur in any cell of the body except germ cells and accordingly, are not passed on to progeny.

[0149] Specifically binds: As used herein, “specifically binds” in the context of an probe or other oligonucleotide and a target sequence means that under appropriate hybridization conditions, the oligonucleotide or probe hybridizes to its target sequence, or replicates thereof, to form a stable probe:target hybrid, while at the same time formation of stable probemon-target hybrids is minimized. Thus, a probe hybridizes to a target sequence or replicate thereof to a sufficiently greater extent than to a non-target sequence, to enable capture or detection of the target sequence. Appropriate hybridization conditions are well-known in the art, may be predicted based on sequence composition, or can be determined by using routine testing methods (see, e.g., Sambrook et al., Molecular Cloning, A Laboratory Manual, 2nded. (Cold Spring Harbor Laboratory Press, Cold Spring Harbor, NY, 1989) at §§ 1.90-1.91 , 7.37-7.57, 9.47-9.51 and 11.47- 11.57, particularly §§ 9.50-9.51 , 11.12-11.13, 11.45-11.47 and 11.55-11.57, incorporated by reference herein).

[0150] Subject: As used herein, “subject” refers to an animal, such as a mammalian species (e.g., human) or avian (e.g., bird) species, or other organism, suchas a plant. More specifically, a subject can be a vertebrate, e.g., a mammal such as a mouse, a primate, a simian or a human. Animals include farm animals (e.g., production cattle, dairy cattle, poultry, horses, pigs, and the like), sport animals, and companion animals (e.g., pets or support animals). A subject can be a healthy individual, an individual that has or is suspected of having a disease or a predisposition to the disease, or an individual that is in need of therapy or suspected of needing therapy. The terms “individual” or “patient” are intended to be interchangeable with “subject.”

[0151] For example, a subject can be an individual who has been diagnosed with having a cancer, is going to receive a cancer therapy, and / or has received at least one cancer therapy. The subject can be in remission of a cancer. As another example, the subject can be an individual who is diagnosed of having an autoimmune disease. As another example, the subject can be a female individual who is pregnant or who is planning on getting pregnant, who may have been diagnosed of or suspected of having a disease, e.g., a cancer, an auto-immune disease.

[0152] Target Region. As used herein, “target region” refers to a genomic locus targeted for identification and / or capture, for example, by using probes (e.g., through sequence complementarity). A Target region set” or “set of target regions" refers to a plurality of genomic loci targeted for identification and / or capture, for example, by using a set of probes (e.g., through sequence complementarity).

[0153] Threshold: As used herein, “threshold” refers to a predetermined value used to characterize experimentally determined values of the same parameter for different samples depending on their relation to the threshold.

[0154] Tumor Fraction: As used herein, “tumor fraction” refers to the estimate of the fraction of nucleic acid molecules derived from a tumor in a given sample. For example, the tumor fraction of a sample can be a measure derived from the max MAF of the sample or pattern of sequencing coverage of the sample or length of the cfDNA fragments in the sample or any other selected feature of the sample. In some instances, the tumor fraction of a sample is equal to the max MAF of the sample.

[0155] Variant: As used herein, a “variant” can be referred to as an allele. A variant is usually presented at a frequency of 50% (0.5) or 100% (1 ), depending on whether the allele is heterozygous or homozygous. For example, germline variants are inherited andusually have a frequency of 0.5 or 1. Somatic variants; however, are acquired variants and usually have a frequency of < 0.5. Major and minor alleles of a genetic locus refer to nucleic acids harboring the locus in which the locus is occupied by a nucleotide of a reference sequence, and a variant nucleotide different than the reference sequence respectively. Measurements at a locus can take the form of allelic fractions (Afs), which measure the frequency with which an allele is observed in a sample.DETAILED DESCRIPTION

[0156] Cancer is usually caused by the accumulation of mutations within genes of an individual’s cells, at least some of which result in improperly regulated cell division. Such mutations can include single nucleotide variations (SNVs), gene fusions, insertions, transversions, translocations, and inversions. These mutations can also include copy number variations that correspond to an increase or a decrease in the number of copies of a gene within a tumor genome relative to an individual’s noncancerous cells. An extent of mutations present in cell-free nucleic acids and an amount of mutated cell-free nucleic acids of a sample can be used as biomarkers to determine tumor progression, predict patient outcome, and refine treatment choices. In various examples, the extent of mutations present in cell-free nucleic acids can be indicated by tumor cells copy number and tumor fraction for a given sample.

[0157] Additionally, cancer can be indicated by non-sequence modifications, such as methylation. Examples of methylation changes in cancer include local gains of DNA methylation in the CpG islands at the TSS of genes involved in normal growth control, DNA repair, cell cycle regulation, and / or cell differentiation. This increased amount of methylation can be associated with an aberrant loss of transcriptional capacity of involved genes and occurs at least as frequently as point mutations and deletions as a cause of altered gene expression.

[0158] Thus, DNA methylation profiling can be used to detect aberrant methylation in DNA of a sample. The DNA can correspond to certain genomic regions (“differentially methylated regions” or “DMRs”) that are normally hypermethylated or hypomethylated in a given sample type (e.g., cfDNA from the bloodstream) but which may show an abnormal degree of methylation that correlates to a neoplasm or cancer, e.g., because of unusuallyincreased contributions of tissues to the type of sample (e.g., due to increased shedding of DNA in or around the neoplasm or cancer) and / or from extents of methylation of the genome that are altered during development or that are perturbed by disease, for example, cancer or any cancer-associated disease.

[0159] Some methods of measuring DNA methylation, can make accurately determining an amount of methylation of DNA difficult. The accuracy with which DNA methylation is determined can impact the accuracy of estimates of tumor fraction for samples. Since tumor fraction can be used to determine whether a sample is derived from a subject in which a tumor is present or not, the accuracy of determination of tumor fraction estimates can impact diagnosis and / or treatment decisions for individuals.

[0160] The methods and systems described herein are directed to accurately generating information indicating the amounts of methylation of nucleic acids using data that indicates an amount of binding of nucleic acids to methyl binding domain (MBD). In various examples, the application is directed to systems and processes to determine an estimate for tumor fraction of a sample. In one or more examples, amounts of methylation of nucleic acids can be determined based on a strength of binding by the nucleic acids to methyl binding domain (MBD). The nucleic acids can be partitioned according to the strength of binding to MBD. Additionally, a number of cytosine-guanine (CG) regions for the nucleic acids can be determined. Amounts of methylation of classification regions of the nucleic acids can be determined based on the partition information associated with the nucleic acids and the number of cytosine-guanine regions of the nucleic acids. The classification regions can have differing amounts of methylation in tumor cells and non- tumor cells. The estimate for tumor fraction of the sample can be determined according to the amounts of methylation of the classification regions.

[0161] In at least some implementations, the methods, systems, techniques, and architectures can implement models that are configured to have at least one of parameters or weights that can be modified to more accurately fit to the methylation data provided to the models. The methods, systems, techniques, and architectures are also directed to implementing a number of optimization procedures during the training of the models to generate models that more accurately predict metrics indicating the presence or absence of tumors than other systems, methods, techniques, and architectures.Further, the methods, techniques, and processes used to generate the information used to produce the methylation data reduce the amount of noise present in the methylation data that leads to more accurate predictions of metrics that indicate the presence or absence of tumors than other methods, techniques, and processes.

[0162] The processes, systems, techniques, methods, frameworks, and architectures described herein are directed to analyzing data generated from biological samples. The amounts of data derived from the biological samples and that corresponds to detectable signals related to the biological samples can be relatively small in relation to the total amount of data derived from the biological samples. Thus, it can be challenging to produce computational models that can reliably detect signals that correspond to one or more biological conditions when the amount of data derived from a sample that can be identified by the computational models as being indicative of a biological condition is relatively small. The importance of producing reliable computational models indicating the presence or absence of a biological condition is high, especially in situations where the biological condition can be detrimental to the health of a subject and / or in situations where healthcare practitioners are making treatment decisions, at least in part, based on the output of the computational models. In many instances, the training process used to produce computational models can have an impact on the accuracy and reliability of the output produced by the computational models. However, training computational models to identify features that are indicative of a biological condition from a relatively small amount of data and / or using data derived from a small number of samples can be challenging. In many typical situations, the amount of data used to train computational models is increased with the intent to increase the accuracy and reliability of the computational models. Yet, simply increasing the amount of data used to train a computational model does not guarantee that the reliability and / or accuracy of the computational model will be improved over versions of the computational model trained with less data.

[0163] At least a portion of the implementations described herein are directed to training computational models using data derived from a relatively small number of biological samples and / or using data with a relatively small proportion that indicates features of the presence of a biological condition within a subject. In various examples,the implementations described herein are directed to identifying one or more subsets of training data from amongst the total data derived from biological samples to produce a computational model that can provide accurate and reliable results indicating the presence or absence of a biological condition within a subject. In one or more examples, training data can be obtained that includes training sequencing reads derived from a plurality of samples of a first plurality of subjects in which a tumor is detected. In at least some examples, the training sequencing reads can correspond to molecules derived from the samples that have at least a threshold amount of methylation in one or more genomic regions. The threshold amount of methylation can correspond to methylated cytosines. Additionally, the training process can use a first computational model and the training data to determine individual values of a quantitative measure for individual samples of the plurality of samples. In one or more illustrative examples, the quantitative measure can indicate an amount of mutant alleles present in nucleic acids derived from the individual samples. For example, the quantitative measure can correlate with the number of mutant alleles present if a mutation is present. In one or more additional illustrative examples, the quantitative measure can include mutant allele fraction. In one or more further illustrative examples, the quantitative measure can indicate a tumor fraction for an individual sample. In some embodiments, the quantitative measure indicating the tumor fraction can be determined via epigenetic analysis like methylation analysis and / or fragmentation pattern analysis or via somatic variant analysis (e..g. maximum mutant allele fraction can be used to indicate the tumor fraction). A subset of the training samples can be determined that have values of the quantitative measure within a specified range of values. An additional group of training samples can be determined that includes samples from the subset of training samples having nucleic acid molecules with one or more somatic mutations present. Further, another group of training samples can be determined from a different group of subjects in which a tumor is not detected. A second computational model can be trained using training data derived from the three groups of training samples. After the training process, the second computational model can be implemented to determine an indication of cancer being present in test subjects.

[0164] In this way, the implementations described herein identify specific datasets from among a larger dataset that are used to train a machine learning classification model.At least a portion of the training datasets are determined based on values of a quantitative measure generated by a different machine learning model that are included in a particular band or range. In various examples, the band or range of quantitative measure values used to determine at least a portion of the training data for the second, machine learning classification model can be based on a biological condition, such as one or more types of cancer being detected. The use of the specific training datasets described in implementations herein to train the machine learning classification model produces a model that is more reliable and provides more accurate results than computational models that are not trained according to implementations described herein. Additionally, because the training of the machine learning classification model is performed using less training data than previously implemented processes, the amount of processing resources and memory resources used to produce the machine learning classification model is less than the previously implemented training processes.

[0165] Figure 1 is a diagrammatic representation of an example environment 100 that identifies nucleic acids that correspond to classification regions of a reference sequence, where the classification regions have at least a threshold number of CpGs, according to one or more implementations. In one or more examples, the disease under consideration is a type of cancer. Non-limiting examples of such cancers include biliary tract cancer, bladder cancer, transitional cell carcinoma, urothelial carcinoma, brain cancer, gliomas, astrocytomas, breast carcinoma, metaplastic carcinoma, cervical cancer, cervical squamous cell carcinoma, rectal cancer, colorectal carcinoma, colon cancer, hereditary nonpolyposis colorectal cancer, colorectal adenocarcinomas, gastrointestinal stromal tumors (GISTs), endometrial carcinoma, endometrial stromal sarcomas, esophageal cancer, esophageal squamous cell carcinoma, esophageal adenocarcinoma, ocular melanoma, uveal melanoma, gallbladder carcinomas, gallbladder adenocarcinoma, renal cell carcinoma, clear cell renal cell carcinoma, transitional cell carcinoma, urothelial carcinomas, Wilms tumor, leukemia, acute lymphocytic leukemia (ALL), acute myeloid leukemia (AML), chronic lymphocytic (CLL), chronic myeloid (CML), chronic myelomonocytic (CMML), liver cancer, liver carcinoma, hepatoma, hepatocellular carcinoma, cholangiocarcinoma, hepatoblastoma, Lung cancer, non-small cell lung cancer (NSCLC), mesothelioma, B-cell lymphomas, non-Hodgkin lymphoma, diffuse large B-cell lymphoma, Mantle cell lymphoma, T cell lymphomas, non-Hodgkin lymphoma, precursor T-lymphoblastic lymphoma / leukemia, peripheral T cell lymphomas, multiple myeloma, nasopharyngeal carcinoma (NPC), neuroblastoma, oropharyngeal cancer, oral cavity squamous cell carcinomas, osteosarcoma, ovarian carcinoma, pancreatic cancer, pancreatic ductal adenocarcinoma, pseudopapillary neoplasms, acinar cell carcinomas. Prostate cancer, prostate adenocarcinoma, skin cancer, melanoma, malignant melanoma, cutaneous melanoma, small intestine carcinomas, stomach cancer, gastric carcinoma, gastrointestinal stromal tumor (GIST), uterine cancer, or uterine sarcoma.

[0166] The environment 100 can include a sample 102. The sample 102 can be derived from a biological fluid obtained from a subject. For example, the sample 102 can be derived from blood obtained from a subject. In one or more additional examples, the sample 102 can be derived from tissue of a subject. In various examples, the sample 102 can be derived from multiple sources. To illustrate, the sample 102 can be derived from one or more fluids of a subject and / or from tissue of a subject. In one or more illustrative examples, the subject can be a mammal. In one or more additional illustrative examples, the subject can be a human. In one or more further illustrative examples, the subject can be a non-human mammal.

[0167] The sample 102 can include a number of nucleic acids 104. Individual nucleic acids 104 can include a number of regions that have at least a threshold number of cytosine molecules and guanine molecules. In one or more examples, individual nucleic acids 104 can include regions having at least a threshold number of cytosine- guanine dinucleotides. In various examples, at least a portion of the cytosine-guanine pairs included in the regions can be sequentially located in sequences of the nucleic acids 104. In one or more illustrative examples, a region of a nucleic acid having at least a threshold amount of cytosine-guanine pairs can be referred to herein as a “CG region” or a “CpG region.” In one or more examples, a CG region can include at least 200 CpG dinucleotides. In one or more illustrative examples, a CG region can include from 200 CpG dinucleotides to 5000 CpG dinucleotides, from 300 CpG dinucleotides to 3000 CpG dinucleotides, from 200 CpG dinucleotides to 2500 CpG dinucleotides, or from 500 CpG dinucleotides to 1500 CpG dinucleotides. Additionally, a CG region can have a GCpercentage of at least 50% and an observed-to-expected CpG ratio of at least 60%. The observed-to-expected CpG ratio can be calculated where the observed CpG is the number of CpGs identified in a given genomic region and the expected CpGs is the number of cytosines multiplied by the number of guanines divided by the number of bases in the genomic region. The expected CpGs can also be calculated by:((number of cytosines + number of guanines) / 2)2 / length of genomic region.For example, a CG region can be determined using the techniques described by Gardiner-Garden M, Frommer M (1987). "CpG islands in vertebrate genomes". Journal of Molecular Biology. 196 (2): 261-282. and / or Saxonov S, Berg P, Brutlag DL (2006). "A genome-wide analysis of CpG dinucleotides in the human genome distinguishes two distinct classes of promoters". Proc Natl Acad Sci USA. 103 (5): 1412-1417.

[0168] In the illustrative example of Figure 1 , a portion of a sequence of an example nucleic acid 104 can include a first CG region 106, a second CG region 108, and a third CG region 110. Although the illustrative example of Figure 1 illustrates a portion of a sequence of a nucleic acid 104 having three CG regions, nucleic acids 104 included in the sample 102 can have a different number of CG regions. For example, individual nucleic acids 104 included in the sample 102 can include at least 1 CG region, at least 5 CG regions, at least 10 CG regions, at least 25 CG regions, at least 50 CG regions, at least 100 CG regions, at least 250 CG regions, at least 500 CG regions, or at least 1000 CG regions.

[0169] Individual CG regions can correspond to a number of molecules with one or more methylated cytosines. In the illustrative example of Figure 1 , the CG region 106 can include a molecule with a methylated cytosine 112. In the illustrative example of Figure 1 , the molecule with a methylated cytosine 112 is 5-methylcytosine. Individual CG regions can also correspond to a number of molecules with an unmethylated cytosine. For example, the CG region 106 can include a molecule with an unmethylated cytosine 116. In various examples, at least a portion of the CG regions of a nucleic acid 104 can correspond to classification regions of a reference genome. Classification regions can correspond to genomic regions of a reference genome that correspond to non-sequence differences that are consistent with one or more biological conditions, such as one or more types of cancer. In at least some examples, the non-sequence differences caninclude one or more mutations that are consistent with one or more biological conditions. In one or more examples, a classification region can correspond to a genomic region of the reference sequence for which molecules derived from subjects having at least one form of cancer. In at least some examples, nucleic acid molecules having at least a threshold amount of methylated cytosines in at least one CG region (e.g., hypermethylated molecules) can be derived from subjects in which cancer is present and correspond to a classification. In one or more additional examples, nucleic acid molecules having less than a threshold amount of methylated cytosines (e.g., hypomethylated molecules) in at least one CG region can be derived from subjects in which cancer is present and correspond to a classification region.

[0170] In addition to the classification regions, the CG regions can include one or more positive control regions, such as positive control region 118. The positive control region 108 can be mapped to nucleic acid molecules having at least a threshold number of methylated cytosine molecules in at least one CG region and that are derived from subjects that are free of cancer and are derived from subjects in which cancer is present. In various examples, the positive control region 106 can be hypermethylated in cells derived from subjects that are free of cancer and also in cells derived from subjects in which cancer is present. The CG regions can also include one or more negative control regions, such as negative control region 120. The negative control region 120 can be mapped to nucleic acid molecules having less than a threshold number of methylated cytosine molecules in at least one CG region and that are derived from subjects that are free of cancer and also subjects in which cancer is present. In one or more illustrative examples, the negative control region 120 can be hypomethylated in subjects that are free of cancer and also in subjects in which cancer is present. In various examples, the positive control regions and the negative control regions can be used to perform normalization calculations. The normalization calculations can be performed to generate input data for one or more models that are implemented to determine tumor metrics for a given sample 102.

[0171] A first molecule separation process 122 can be performed. The first molecule separation process 122 can separate nucleic acids 104 included in the sample 102 based on an amount of methylated cytosines of the individual nucleic acids 104. Inone or more examples, the first molecule separation process can separate nucleic acids 104 included in the sample 102 based on amounts of methylated cytosines included in CG regions of individual nucleic acids 104. In various examples, the first molecule separation process 122 can separate the nucleic acids 104 into a plurality of groups with individual groups corresponding to respective amounts of methylated cytosines of the nucleic acids 104.

[0172] In the illustrative example of Figure 1 , the first molecule separation process 122 can be performed in relation to a first methylation threshold 124. Performing the first molecule separation process 122 with regard to the first methylation threshold 124 can produce a first partition of nucleic acids 126. In one or more examples, the first methylation threshold 124 can indicate a first threshold number of molecules with a methylated cytosine located in CG regions of the nucleic acids 104. The first molecule separation process 122 can identify a number of nucleic acids 104 having fewer molecules with a methylated cytosine in CG regions than the first methylation threshold 124. In various examples, the first methylation threshold 124 can correspond to a first methylation rate.

[0173] The first molecule separation process 122 can also be performed with respect to a second methylation threshold 128. The second methylation threshold 128 can indicate an amount of methylated cytosines in one or more genomic regions of the nucleic acids 104 that is greater than the amount of methylated cytosines in the one or more regions corresponding to the first methylation threshold 124. The second methylation threshold 124 can indicate a number of molecules with a methylated cytosine per a number of nucleic acids. In one or more additional examples, the second methylation threshold 124 can correspond to a rate of methylation of nucleic acids that is greater than the rate of methylation that corresponds to the first methylation threshold 124. Performing the first molecule separation process 122 with respect to the second methylation threshold 128 can produce a second partition of nucleic acids 130. In one or more examples, the first molecule separation process 122 can identify nucleic acids 104 having a greater amount of methylated cytosines than the first methylation threshold 124 and having a lower amount of methylated cytosines than the second methylation threshold 128 to produce the second partition of nucleic acids 130.

[0174] Additionally, the first molecule separation process 122 can also be performed with respect to a third methylation threshold 132. The third methylation threshold 132 can indicate an amount of methylated cytosines in one or more genomic regions of the nucleic acids 104 that is greater than the amount of methylated cytosines in the one or more regions corresponding to the first methylation threshold 124 and greater than the amount of methylated cytosines in the one or more regions corresponding to the second methylation threshold 128. The third methylation threshold 132 can indicate a number of molecules with a methylated cytosine per a number of nucleic acids. In one or more additional examples, the third methylation threshold 132 can correspond to a rate of methylated cytosines that is greater than the rate of methylation that corresponds to the first methylation threshold 124 and greater than the rate of methylation that corresponds to the second methylation threshold 128. Performing the first molecule separation process 122 with respect to the third methylation threshold 132 can produce a third partition of nucleic acids 134. In one or more examples, the first molecule separation process 122 can identify nucleic acids 104 having a greater amount of methylated cytosines than nucleic acids 104 included in the second partition of nucleic acids 128. In this way, the amount of methylated cytosines of nucleic acids included in the first partition 122, the second partition 126, and the third partition 130 increases from the first partition 122 to the second partition 126 and increases from the second partition 126 to the third partition 130. In one or more illustrative examples, the first partition of nucleic acids 126 can be referred to as a hypomethylation partition, the second partition of nucleic acids 130 can be referred to as an intermediate partition, and the third partition of nucleic acids 134 can be referred to as a hypermethylation partition.

[0175] In one or more examples, the amount of methylated cytosines of nucleic acids can correspond to a strength of binding to methyl binding domain (MBD). In these scenarios, the first partition 126, the second partition 130, and the third partition 134 can be produced based on different strengths of binding to MBD for nucleotides having different amounts of methylated cytosines. In one or more examples, the first molecule separation process 122 can include a series of washes where the nucleic acids 104 are contacted with solutions having different concentrations of sodium chloride (NaCI).

[0176] Partitioning of the nucleic acids can be performed by contacting the nucleic acids with a modified nucleotide specific binding reagent, such as a MBD of a MBP. A modified nucleotide specific binding reagent can bind to 5-methylcytosine (5mC). The modified nucleotide specific binding reagent, such as a MBD, can be coupled to paramagnetic beads, such as Dynabeads® M-280 Streptavidin via a biotin linker. Partitioning into fractions with different extents of methylation can be performed by increasing the NaCI concentration in a series of washes. The sequences eluted from the modified nucleotide specific binding reagent are partitioned into two or more fractions (e.g., hypo, hyper) depending on which wash (e.g., NaCI concentration) eluted the sequences. Resulting partitions can include one or more of the following nucleic acid forms: double-stranded DNA (dsDNA), shorter DNA fragments and longer DNA fragments.

[0177] The binding of the nucleic acids with the modified nucleotide specific binding reagent can be a function of number of methylated (or modified) sites per molecule, with molecules having more methylation eluting under increased salt concentrations. To elute the DNA into distinct populations based on the extent of methylation, one can use a series of elution buffers of increasing NaCI concentration. Salt concentrations can, in one or more implementations, range from about 100 nM to about 2500 mM NaCI. In various implementations, the process results in three (3) partitions. Molecules are contacted with a solution at a first salt concentration and comprising a molecule comprising a methyl binding domain, which molecule can be attached to a capture moiety, such as streptavidin. At the first salt concentration a population of molecules will bind to the MBD and a population will remain unbound. The unbound population can be separated as a “hypomethylated” population (hypo partition). For example, the first partition 126 can be representative of the hypomethylated form of DNA is that which remains unbound at a low salt concentration. In one or more illustrative examples, the concentration of NaCI of the solution used to produce the first partition 126 can be about 100 nM, about 120 nM, about 140 nM, about 160 nM, about 180 nM, about 200 nM. or about 250 nM. The second partition 130 can be referred to as a “residual partition” or an “intermediate partition” and can be representative of intermediate methylated DNA is eluted using an intermediate salt concentration, e.g., between 100 mM and 2000 mM concentration. In one or moreadditional illustrative examples, the concentration of NaCI of the solution used to produce the second partition 130 can be from about 100 mM to about 500mM, from about 100 mM to about 1000 mM, from about 100 mM to about 1500 mM, from about 250 mM to about 1000 mM, from about 250 mM to about 1500 mM, from about 500 mM to about 1500 mM, from about 250 mM to about 2000 mM, from about 500 mM to about 2000 mM, or from about 1000 mM to about 2000mM. This is also separated from the sample. The third partition 134 can be representative of hypermethylated form of DNA (hyper partition) and is eluted using a high salt concentration, e.g., at least about 2000 mM. In one or more further illustrative examples, the concentration of NaCI of the solution used to produce the third partition 134 can be from about 2000 mM to about 5000 mM, from about 2000 mM to about 4000 mM, from about 2000 mM to about 3500 mM, from about 2000 mM to about 3000 mM, or from about 2500 mM to about 4000 mM.

[0178] In various examples, the first partition 126 can correspond to a first range of binding strengths of nucleic acids to MBD and to a first range of methylated CG regions and the second partition 130 can correspond to a second range of binding strengths of nucleic acids to MBD and to a second range of methylated CG regions. The first range of binding strengths can be less than the second range of binding strengths. In one or more scenarios, a first solution having a first NaCI concentration can separate a first group of nucleic acids having the first range of binding strengths from MBD and a second solution having a second NaCI concentration can separate a second group of nucleic acids having the second range of binding strengths from MBD with the second NaCI concentration being greater than the first NaCI concentration. Additionally, the third partition 134 can correspond to a third range of binding strengths and a third range of methylated CG regions. The third range of binding strengths can be greater than the first range of binding strengths and the second range of binding strengths. In one or more instances, a third solution having a third NaCI concentration can separate a third group of nucleic acids having the third range of binding strengths from NaCI. The third NaCI concentration can be greater than the first NaCI concentration and the second NaCI concentration.

[0179] In one or more illustrative examples, a plurality of nucleic acids derived from at least one of blood or tissue of a subject can be combined with a solution including an amount of MBD to produce a nucleic acid-MBD solution. A first wash of the nucleic acid-MBD solution can be performed with a first solution including a first NaCI concentration to produce a first nucleic acid fraction and a first residual solution. The first nucleic acid fraction can include a first portion of the plurality of nucleic acids and the first residual solution can include a second portion of the plurality of nucleic acids. In one or more examples, the first portion of the plurality of nucleic acids can have a first range of binding strengths to MBD that are less than a second range of binding strengths to MBD of the second portion of the plurality of nucleic acids.

[0180] Additionally, a second wash of the first residual solution can be performed with a second solution including a second concentration of NaCI that is greater than the first concentration of NaCI to produce a second nucleic acid fraction and a second residual solution. The second nucleic acid fraction can include a first subset of the second portion of the plurality of nucleic acids and the second residual solution can include a second subset of the second portion of the plurality of nucleic acids. The first subset of the second portion of the plurality of nucleic acids can have a third range of binding strengths to MBD that are less than a fourth range of binding strengths to MBD of the second subset of the second portion of the plurality of nucleic acids. Further, a third wash of the second residual solution can be performed with a third solution including a third concentration of NaCI that is greater than the second concentration of NaCI to produce a third nucleic acid fraction that includes the second subset of the second portion of the plurality of nucleic acids.

[0181] Subsequent to the first wash, the second wash, and the third wash a determination can be made that the first portion of the plurality of nucleic acids are associated with the first partition 126. The first portion of the plurality of nucleic acids can be attached with molecular barcodes from a first set of molecular barcodes indicating the first partition 126. In this way, a sequencing read that corresponds to the first partition 126 can be identified based on determining that the sequencing read includes the first molecular barcode. In addition, a determination can be made that the first subset of the second portion of the plurality of nucleic acids is associated with an additional partition of the plurality of partitions. In these situations, a second set of molecular barcodes different from the first set of molecular barcodes can be attached to the second portion of the plurality of nucleic acids with the second molecular barcode indicating the additional partition. As a result, a sequencing read that corresponds to the additional partition canbe identified based on determining that the sequencing read includes one or more molecular barcodes from among the second set of molecular barcodes. Further, a determination can be made that the second subset of the second portion of the plurality of nucleic acids is associated with the second partition 130. A third set of molecular barcodes different from the first set of molecular barcodes and the second set of molecular barcodes can then be attached to the second subset of the second portion of the plurality of nucleic acids where the third set of molecular barcodes indicate the second partition 130. In these instances, a sequencing read that corresponds to the second partition 130 can be identified based on determining that the sequencing read includes a third molecular barcode from among the third set of molecular barcodes.

[0182] In at least some examples, the first molecule separation process 122 can result in nucleic acids being present in at least one of the first partition 126, the second partition 130, or the third partition 134 having an amount of methylation that is different from the amount of methylation of the other nucleic acids in the respective partition. For example, the first partition 126 can include a number of nucleic acids having amounts of methylation that correspond to the amounts of methylation of nucleic acids included in at least one of the second partition 130 or the third partition 134. Additionally, at least one of the second partition 130 or the third partition 134 can include nucleic acids having amounts of methylation that correspond to the amounts of methylation of nucleic acids included in the first partition 126. The presence of nucleic acids in at least one of the first partition 126, the second partition 130, or the third partition 134 that do not correspond to the amounts of methylation of at least a majority of the other nucleic acids included in the respective partition can cause data noise when performing computational operations with respect to sequence reads produced from nucleic acids included in the first partition 126, the second partition 130, and the third partition 134. The data noise can result in inaccuracies with respect to calculations made based on sequence reads derived from nucleic acids included in the first partition 126, the second partition 130, and the third partition 134.

[0183] To reduce or eliminate data noise associated with nucleic acids being present in at least one of the first partition 126, the second partition 130, or the third partition 134 that have amounts of methylation that are not consistent with the amountsof methylation of at least a majority of other molecules included in the respective partitions, a second molecule separation process 136 can be performed after the first molecule separation process 122. The second molecule separation process 136 can be performed with respect to nucleic acids included in the first partition 126, nucleic acids included in the second partition 130, and nucleic acids included in the third partition 134. In one or more examples, the second molecule separation process 136 can include performing digestion of the nucleic acids included in the first partition 126 using methylation dependent restriction enzyme (MDRE) and nucleic acids included in the second partition 130 and the third partition 134 can be digested using methylation sensitive restriction enzyme (MSRE). Digestion of the nucleic acids included in the first partition 126 with MDRE can result in separation of nucleic acids included in the first partition having amounts of methylation corresponding to the second partition 130 and the third partition 134 from nucleic acids having amounts of methylation corresponding to the first partition. Additionally, digestion of nucleic acids included in the second partition 130, and the third partition 134 with MSRE can result in separation of the nucleic acids having amounts of methylation corresponding to the first partition 126 from the nucleic acids of the second partition 130 and the nucleic acids of the third partition 134. By removing nucleic acids from the first partition 126 having amounts of methylation that correspond to the second partition 130 and the third partition 134 and by removing nucleic acids from the second partition 130 and the third partition 134 that have amounts of methylation that correspond to the first partition 126, an additional group of nucleic acids 138 can be produced. The additional group of nucleic acids 138 can include nucleic acids corresponding to methylation amounts of the second partition 130 and the third partition 134 with a minimal amount or no nucleic acids having amounts of methylation corresponding to the first partition 126. For example, less than 50% of the nucleic acids included in the additional group 138 can have amounts of methylation that correspond to the second partition 130 and the third partition 134, at least 50% of the nucleic acids included in the additional group 138 can have amounts of methylation that correspond to the second partition 130 and the third partition 134, at least 60% of the nucleic acids included in the additional group 138 can have amounts of methylation that correspond to the second partition 130 and the third partition 134, at least 70% of the nucleic acidsincluded in the additional group 138 can have amounts of methylation that correspond to the second partition 130 and the third partition 134, at least 90% of the nucleic acids included in the additional group 138 can have amounts of methylation that correspond to the second partition 130 and the third partition 134, at least 95% of the nucleic acids included in the additional group 138 can have amounts of methylation that correspond to the second partition 130 and the third partition 134, at least 97% of the nucleic acids included in the additional group 138 can have amounts of methylation that correspond to the second partition 130 and the third partition 134, at least 99% of the nucleic acids included in the additional group 138 can have amounts of methylation that correspond to the second partition 130 and the third partition 134, at least 99.5% of the nucleic acids included in the additional group 138 can have amounts of methylation that correspond to the second partition 130 and the third partition 134, or at least 99.9% of the nucleic acids included in the additional group 138 can have amounts of methylation that correspond to the second partition 130 and the third partition 134.

[0184] The architecture 100 can include a sequencing machine 140. In one or more examples, the sequencing machine 140 can be any of a number of sequencing machines that can perform one or more sequencing operations that amplify nucleic acids present in a sample 104. In various examples, the sequencing machine 140 can perform next- generation sequencing operations. In one or more examples, the sample 104 can include an amount of at least one bodily fluid extracted from a subject. In one or more additional examples, the sample 104 can include a tissue sample that is obtained from a subject.

[0185] In one or more examples, prior to sequencing, the extracted polynucleotides can be partitioned into two or more partitions based on the binding strength of the of binding strengths of polynucleotides to MBD. A blunt-end ligation can be performed on the partitioned polynucleotides and adapters, as well as tags (e.g., molecular barcodes) can be added to the partitioned polynucleotides. The tagged polynucleotides in the one or more partitions (e.g., hyper and / or intermediate partitions) can be treated with one or more methylation sensitive restriction enzymes (MSREs). In some examples, the hypo partition can be treated with one or more methylated dependent restriction enzymes (MDREs). Post the MSRE and / or MDRE treatment, the molecules can also be enriched by causing hybridization between the extracted polynucleotides and probes thatcorrespond to target regions of a reference sequence. The enrichment process can identify thousands, hundreds of thousands, up to millions of polynucleotides that correspond to on-target regions associated with the probes.

[0186] Subsequent and / or prior to the enrichment process, the molecules can be amplified according to one or more amplification processes. The one or more amplification processes can produce thousands, up to millions of copies of individual nucleic acid molecules. In one or more examples, a portion of the unenriched polynucleotides can be amplified, in some instances, but not to the extent that the enriched polynucleotides are amplified. The one or more amplification processes can generate an amplification product that undergoes one or more sequencing operations. After performing one or more sequencing operations with respect to the sample 104, the sequencing machine 140 can produce a sequencing data 142.

[0187] The sequencing data 142 can include alphanumeric representations of the nucleic acids included in an amplification product. For example, the sequencing data 142 can include, for individual nucleic acids of the amplification product, data that corresponds to a string of letters that represent the respective chains of nucleotides that correspond to the individual nucleic acids.

[0188] The sequencing data 142 can be stored in one or more data files. For example, the sequencing data 142 can be stored in a FASTQ file that comprises a text- based sequencing data file format storing raw sequence data and quality scores. In one or more additional examples, the sequencing data 142 can be stored in a data file according to a binary base call (BCL) sequence file format. In one or more further examples, the sequencing data 142 can be stored in a BAM file. In one or more examples, the sequencing data 142 can comprise at least about one gigabyte (GB), at least about 2 GB, at least about 3GB, at least about 4 GB, at least about 5 GB, at least about 8 GB, or at least about 10 GB. An individual sequence representation included in the sequencing data 106 can be referred to herein as a “read” or a “sequencing read.” In various examples, individual first nucleic acids included in the pool 138 can correspond to multiple sequence representations included in the sequencing data 142 as a result of the amplification of the individual first nucleic acids. In one or more additional examples, individual second nucleic acids included in the pool 138 can correspond to a singlesequence representation included in the sequencing data 142 as a result of the absence of amplification of the individual second nucleic acids.

[0189] FIG. 2 is an example architecture 200 to analyze sequencing data to determine one or more metrics indicating the presence of a tumor in subjects, in accordance with one or more implementations. The architecture 200 can include one or more sequencing machines 202 that perform one or more sequencing operations with respect to a number of samples 204. The one or more samples 204 can be obtained from subjects 206. In one or more illustrative examples, a first portion of the subjects 206 can be free of cancer. That is, a tumor is not detected in the first portion of the subjects 206. Additionally, a tumor can be present in a second portion of the subjects 206.

[0190] One or more molecule separation processes 208 can be performed with respect to the samples 204. The one or more separation processes 208 can correspond to separating nucleic acid molecules into a number of partitions based on the characteristics of the nucleic acid molecules. Examples of characteristics that can be used for partitioning nucleic acid molecules include multiple different nucleotide modifications, methylation level, nucleosome binding, sequence mismatch, immunoprecipitation, and / or proteins that bind to DNA. In one or more illustrative examples, a heterogeneous population of nucleic acid molecules can be partitioned into nucleic acid molecules with one or more epigenetic modifications and without the one or more epigenetic modifications. Examples of epigenetic modifications include, but are not limited to, presence or absence of methylation; level of methylation, hydroxymethylation, and type of methylation (5' cytosine or 6 methyladenine).

[0191] Prior to the one or more molecule separation processes 208, nucleic acid molecules can be extracted from a sample 204. In one or more implementations, the nucleic acid molecules comprise cell-free nucleic acids (e.g., cell-free DNA). In various implementations, the sample 204 can be a sample selected from one or more of blood, plasma, serum, urine, fecal, saliva samples, combinations thereof, and / or the like. In one or more additional examples, the sample 204 can comprise a sample selected from one or more of whole blood, a blood fraction, a tissue biopsy, pleural fluid, pericardial fluid, cerebrospinal fluid, and peritoneal fluid. In one or more illustrative examples, the cell-free nucleic acid molecules can be extracted from the sample 204 where the sample 204 isobtained from a subject 206 known to have cancer (e.g., a cancer patient), or a subject 206 suspected of having cancer.

[0192] The extraction of nucleic acid molecules from the sample 204 can include implementing one or more cell lysis techniques to cleave the membranes of cells included in the sample 204 and applying one or more proteases to break down proteins included in the sample 204. The extraction of nucleic acid molecules from the sample 204 can also include a number of washing and / or elution techniques to separate the nucleic acid molecules from other components included in the sample 204. In various examples, thousands, up to millions, up to billions of nucleic acid molecules can be extracted from the sample 204 prior to being subjected to the one or more separation processes 208.

[0193] The nucleic acid molecules extracted from samples 204 can include molecules having varying levels of methylation. Methylation can occur from any one or more post-replication or transcriptional modifications. Post-replication modifications include modifications of the nucleotide cytosine, including, but not limited to, 5- methylcytosine, 5-hydroxymethylcytosine, 5-formylcytosine and 5-carboxylcytosine. The one or more molecule separation processes 208 can separate nucleic acid molecules extracted from samples 204 into a number of partitions with individual partitions corresponding to different levels of methylation. For example, the molecule separation processes 208 can produce a first partition of nucleic acid molecules having first levels of methylation, a second partition of nucleic acid molecules having second levels of methylation, and a third partition of nucleic acid molecules having third levels of methylation. In various examples, the second levels of methylation can be greater than the first levels of methylation and the third levels of methylation can be greater than the first levels of methylation and the second levels of methylation. In one or more illustrative examples, the one or more molecule separation processes 208 can include the first molecule separation process 122 and the second molecule separation process 136 of Figure 1.

[0194] The one or more molecule separation processes 208 can produce a pool 210 that includes a portion of the nucleic acid molecules extracted from one or more samples 204 and subjected to the one or more molecule separation processes 208. For example, the pool 210 can include a number of nucleic acid molecules having the secondlevels of methylation and a number of nucleic acid molecules having the third levels of methylation. Thus, the nucleic acid molecules included in the pool 210 can have at least a threshold amount of methylation. In one or more illustrative examples, the nucleic acid molecules included in the pool 210 can have at least a threshold amount of methylation in CG regions of the nucleic acid molecules.

[0195] The one or more sequencing machines 202 can perform one or more sequencing operations to produce sequencing data 212 that corresponds to the pool 210. The architecture 200 can include a computing system 214 that obtains the sequencing data 212 from the one or more sequencing machines 202 and analyzes the sequencing data 212. For example, the computing system 214 can analyze the sequencing data 212 to determine one or more metrics indicating that a tumor may be present in a subject 206 that provided at least one sample 204. The computing system 214 can include one or more computing devices 216. The one or more computing devices 216 can include at least one of one or more desktop computing devices, one or more mobile computing devices, or one or more server computing device. In various examples, at least a portion of the one or more computing devices 216 can be included in a remote computing environment, such as a cloud computing environment. In one or more examples, the computing system 214 and the sequencing machine 202 can be owned, operated, maintained, and / or controlled by a single organization. In one or more additional examples, the computing system 214 and the sequencing machine 202 can be owned, operated, maintained, and / or controlled by multiple organizations.

[0196] At operation 218, the computing system 214 can analyze the sequencing data 212. Analyzing the sequencing data 212 can include determining one or more first sequence representations 220 included in the sequencing data 212 that correspond to one or more classification regions of a reference sequence. The one or more classification regions can correspond to genomic regions of a reference sequence that are mapped to nucleic acid molecules having an amount of methylation in cfDNA obtained from subjects in which cancer is present relative to an amount of methylation of the molecules that map to the same genomic regions of the reference sequence in cfDNA obtained from subjects in which a tumor is not present. In at least some examples, the amount of methylation present in nucleic acid molecules that map to a classification region and are derived fromsubjects in which cancer is present is less than the amount of methylation present in nucleic acid molecules that map to the classification region and are derived from subjects in which cancer is not present. In one or more additional examples, the amount of methylation present in nucleic acid molecules that map to a classification region and are derived from subjects in which cancer is present is greater than the amount of methylation present in nucleic acid molecules that map to the classification region and are derived from subjects in which cancer is not present. The one or more classification regions can also include at least a threshold amount of cytosine-guanine content. In various examples, the one or more classification regions can include a series of cytosine-guanine (CG) pairs in the 5’— >3’ direction (CpG sites), such as at least 3 CpG sites, at least 5 CpG sites, at least 8 CpG sites, at least 10 CpG sites, at least 12 CpG sites, at least 15 CpG sites, at least 18 CpG sites, or at least 20 CpG sites.

[0197] In addition, the computing system 214 can analyze the sequencing data 212 to determine one or more second sequence representations 222 that correspond to one or more control regions of a reference sequence. The one or more control regions can include one or more positive control regions and / or one or more negative control regions. In various examples, a positive control region can comprise a genomic region of a reference sequence having at least a threshold amount of molecules with a methylated cytosine and including at least a threshold number of CpG sites. A positive control region can correspond to nucleic acid molecules having at least a threshold amount of methylation in one or more CG regions and that are obtained from subjects in which cancer is present and in samples obtained from subjects in which a tumor is not present. In at least some examples, the threshold amount of methylation can correspond to at least 5, at least 6, at least 7, at least 8, at least 9, at least 10, at least 11 , at least 12, at least 15 or more CpGs being methylated in nucleic acid molecules. In one or more illustrative examples, positive control regions can be mapped to nucleic acid molecules that are hypermethylated in one or more CG regions and are derived from samples obtained from both subjects in which cancer is present and subjects in which cancer is not present. In one or more examples, a negative control region can comprise a genomic region of a reference sequence having less than a threshold amount of molecules with a methylated cytosine and at least a threshold number of CpG sites. A negative controlregion can correspond to nucleic acid molecules having less than an additional threshold amount of methylation in one or more CG regions and that are obtained from subject in which cancer is present and in samples obtained from subjects in which a tumor is not present. In various examples, the additional threshold amount of methylation can correspond to no greater than 1, no greater than 2, no greater than 3, no greater than 4, no greater than 5, no greater than 6, or no greater than 7 CpGs being methylated in nucleic acid molecules. In one or more additional illustrative examples, negative control regions can be mapped to nucleic acid molecules that are hypomethylated in one or more CG regions and are derived from samples obtained from both subjects in which cancer is present and subjects in which cancer is not present.

[0198] In one or more illustrative examples, the first sequence representations 220 can be determined by aligning sequence representations included in the sequencing data 212 with one or more classification regions of a reference sequence. In addition, the second sequence representations 222 can be determined by aligning sequence representations included in the sequencing data 212 with one or more control regions of a reference sequence. The alignment process can identify the first sequence representations 220 by determining a number of sequence representations included in the sequencing data 212 that correspond to one or more classification regions of the reference sequence. Further, the alignment process can identify the second sequence representations 222 by determining a number of sequence representations that correspond to one or more control regions of the reference sequence.

[0199] In one or more illustrative examples, the alignment process can determine an amount of homology between individual sequence representations included in the sequence data 212 and portions of the reference sequence. The amount of homology between a given sequence representation and the reference sequence can indicate a number of positions of the reference sequence that have the same nucleotide as corresponding positions of the given sequence representation. The computing system 214 can determine that a sequence representation is aligned with a portion of a reference sequence based on determining that the sequence representation and the portion of the reference sequence have at least a threshold amount of homology. In scenarios where a sequence representation has at least the threshold amount of homology with respect tomultiple portions of the reference sequence, the portion of the reference sequence having the greatest amount of homology with the sequence representation can be determined to be aligned with the sequence representation.

[0200] The amount of homology between a given sequence representation and a portion of a reference sequence can be determined using BLAST programs (basic local alignment search tools) and PowerBLAST programs (Altschul et al., J. Mol. Biol., 1990, 215, 403-410; Zhang and Madden, Genome Res., 1997, 7, 649-656) or by using the Gap program (Wisconsin Sequence Analysis Package, Genetics Computer Group, University Research Park, Madison Wis.), using default settings, which uses the algorithm of Needleman and Wunsch (J. Mol. Biol. 48; 443-453 (1970)).The amount of homology between a sequence representation and a portion of the reference sequence can also be determined using a Burrows-Wheeler aligner (Li, H., & Durbin, R. (2009). Fast and accurate short read alignment with Burrows-Wheeler transform. Bioinformatics, 25(14), 1754-1760).

[0201] In one or more examples, after the sequence representations included in the sequencing data 212 have been aligned with a reference sequence, the aligned sequence representations can be analyzed to identify one or more groups of sequence representations. For example, individual aligned sequence representations can correspond to individual sequencing reads that are included in the sequencing data 212. In these scenarios, the aligned sequence representations can include multiple reads that correspond to a single nucleic acid molecule included in the sample pool 210. In one or more additional examples, the aligned sequence representations can correspond to individual nucleic acid molecules included in the pool 210. In these situations, the computing system can determine a group of reads included in the sequence data 212 that correspond to an individual nucleic acid molecule included in the pool 210 based on molecular barcodes that are common to each group of sequencing reads. That is, individual nucleic acid molecules included in the pool 210 can be encoded with molecular barcodes that uniquely identify the individual nucleic acid molecules and, in at least some cases, the individual nucleic acid molecules can be represented by multiple sequencing reads included in the sequencing data 212. Accordingly, when multiple sequence representations are present in the sequencing data 212 that correspond to a singlenucleic acid molecule included in the pool 210, the computing system 214 can group the multiple sequence representations together. In various examples, the groups of sequence representations that correspond to a single nucleic acid molecule included in the pool 210 can be referred to herein as “families.” Additionally, start and stop positions with respect to the reference sequence of the aligned sequence representations having a common molecular barcode can be used to group the sequence representations that correspond to individual nucleic acids included in the pool 210. In one or more illustrative examples, an individual sequence representation that represents a family of sequence representations that corresponds to a single nucleic acid molecule included in the pool 210 can be referred to herein as a “consensus sequence representation.”

[0202] At operation 224, the computing system 214 can analyze the first sequence representations and the second sequence representations 222 to generate metrics that correspond to individual classification regions. In the illustrative example of Figure 2, the computing system 214 can analyze the first sequence representations 220 and the second sequence representations 222 to generate classification region metrics 226. The classification region metrics 226 can include quantitative measures determined based on a number of first sequence representations 220 having at least a threshold amount of methylated cytosines. In one or more illustrative examples, the classification region metrics 226 can include quantitative measures determined based on a number of sequencing reads corresponding to a number of the first sequence representations 220 having at least a threshold amount of methylated cytosines located. In one or more additional illustrative examples, the classification region metrics 226 can include quantitative measures determined based on a number of nucleic acid molecules that correspond to a number of the first sequence representations 220. In various examples, the classification region metrics 226 can include quantitative measures determined based on a number of first sequence representations 220 having at least a threshold amount of methylated cytosines and a number of second sequence representations 222 that correspond to control regions of a reference sequence. In one or more further illustrative examples, the classification region metrics 226 can include quantitative measures related to a ratio of a number of first sequence representations 220 having at least a threshold amount of methylated cytosines in relation to a number of second sequencerepresentations. In at least some examples, the sequence representations of the second sequence representations 222 used by the computing system 214 to generate quantitative measures included in the classification region metrics 226 can include sequence representations that correspond to positive control regions of a reference sequence.

[0203] The classification region metrics 226 can also be determined by performing one or more normalization operations with respect to quantitative measures generated by the computing system 214 using at least one of the first sequence representations 220 and the second sequence representations 222. For example, a logarithm calculation can be performed with respect to quantitative measures generated by the computing system 214 using at least one of the first sequence representations 220 or the second sequence representations 222. Additionally, the classification region metrics 226 can be determined by adding a pseudocount to quantitative measures determined by the computing system 214 using at least one of the first sequence representations 220 or the second sequence representations 222. In one or more illustrative examples, the one or more normalization operations can include determining quantitative measures that correspond to a ratio of first sequence representations 220 for an individual classification region with respect to a number of second sequence representations 222 that correspond to positive control regions of a reference sequence.

[0204] In one or more illustrative examples, the computing system 214 can determine a number of the first sequence representations 220 that correspond to individual classification regions of a reference sequence and that have at least a threshold amount of methylated cytosines located in the individual classification regions. In these scenarios, the computing system 214 can determine individual classification region metrics 226 for individual classification regions. In addition, the computing system 214 can determine a number of the second sequence representations 222 that correspond to positive control regions. In at least some examples, the computing system 214 can, for individual classification regions, determine a ratio including a number of first sequence representations 220 that correspond to the individual classification region and that have at least a threshold amount of molecules with a methylated cytosine in the classification region in relation to a total number of the second sequence representations 222 thecorrespond to positive control regions of a reference sequence. In one or more examples, the computing system 214 can add a value of a pseudocount to the ratio to determine a classification region metric 226 for the individual classification region. The value of the pseudocount can be at least 1 , at least 1.2, at least 1.4, at least 1.6, at least 1.8, or at least 2. Further, the computing system 214 can perform a log base 10 operation with respect to the combination of the ratio and the pseudocount to determine a classification region metric 226 for an individual classification region. In at least some illustrative examples, the computing system 214 can determine at least a portion of the classification region metrics according to the following equation:where x, is a total number of first sequence representations 220 for an individual classification region, i, having at least a threshold amount of methylated cytosines included in the region, I, and xPositive_contmi is a total number of the second sequence representations 222 that correspond to positive control regions of a reference sequence.

[0205] At operation 228, the computing system 214 can execute a model to determine an indication of cancer based on the classification region metrics 226. In the illustrative example of Figure 2, the computing system 214 can execute a model using the classification region metrics 226 to generate model output 230. In one or more examples, the model output 230 can indicate a status of tumor detection 232 or a status of tumor not detected 234 in relation to a sample 204 provided by a subject 206. In one or more additional examples, the computing system 214 can execute a model to determine an estimate of tumor fraction 236 for a sample 204. In one or more further examples, the computing system 214 can execute a model to determine a probability of a tumor being present in a subject 206 that provided a sample 204.

[0206] In one or more examples, the model can include a classification model that implements one or more machine learning techniques. In one or more illustrative examples, the model can include a linear regression model. In various examples, the model can be executed to determine a probability of a tumor being present 238 in a subject 206 that provided a sample 204 based on the classification region metrics 226. Inone or more illustrative examples, the computing system 214 can execute the model to determine weights for individual classification regions. The weights for individual classification regions can be different. For example, the computing system 214 can determine that a first weight of a first classification region metric 226 for a first classification region is different from a second weight of a second classification region metric 226 for a second classification region. In at least some illustrative examples, a probability of a tumor being present 238 in a subject 206 that provided a sample 204 can be determined by the computing system 214 by executing a model that corresponds to the following equation:where w, is a weight of an individual classification region, the score of the region i is calculated using Equation (1 ), and b is a slope corresponding to a linear regression model. In at least some examples, the probability of a tumor being present 238 can be used to generate a status of tumor detected 232 or a status of tumor not detected 234. In one or more further illustrative examples, the computing system 214 can analyze the probability of a tumor being present 238 with respect to a threshold probability to determine a status of tumor detected 232 or a status of tumor not detected 234 for a sample 204. The computing system 214 can determine that a sample 204 corresponds to the status of tumor detected 232 in response to determining that a probability of a tumor being present 238 for the sample 204 is at least the threshold probability. Additionally, the computing system 214 can determine that a sample 204 corresponds to the status of tumor not detected 234 in response to determining that a probability of a tumor being present 238 for the sample 204 is less than the threshold probability.

[0207] In one or more additional examples, the computing system 214 can execute a model that determines a maximum mutant allele fraction (MAF). In various examples, the computing system 214 can execute a model using the maximum MAF value to determine tumor fraction 236 for a sample 204. In one or more illustrative examples, the computing system 214 can execute a model using the classification region metrics 226 to determine a logit transformed maximum MAF value that can then be used by the computing system 214 to estimate tumor fraction for a sample 204. In various examples,the computing system 214 can analyze maximum MAF values to determine a probability of cancer being present 238 in a subject 206 that provided a sample 204. In various examples, a Huber regression (Huber, P. J. 1964. “Robust Estimation of a Location Parameter.” Annals of Mathematical Statistics 35 (1): 73-101) can be performed to determine a maximum MAF value based on the classification region metrics 226.

[0208] In various examples, the model output 230 can also include a tumor tissue indication 240. The tumor tissue indication 240 can indicate one or more tissues from which cancer cells that produced genomic material detected in the sample 204 originate. In one or more examples, the tumor tissue indication 240 can correspond to one or more tissues of origin for cancer cells that produced genomic material detected in the sample 204. In these scenarios, the computing system 214 can generate multiple models with individual models corresponding to a given tissue type. The output from individual models can be analyzed to determine additional metrics that indicate a tissue from which cancer cells that produced genomic material detected in one or more samples originate. In at least some examples, the output for the individual models can indicate at least one of tumor fraction 236 or a probability of tumor being present 238. The computing system 214 can analyze the respective model outputs to determine the model having at least one of a greatest value for tumor fraction or a greatest probability of cancer being present. The computing system 214 can then generate a tumor tissue indication 240 that corresponds to the model having the greatest value for tumor fraction and / or a greatest probability of cancer being present.

[0209] For example, samples 204 can be obtained from subjects 206 in which different types of cancer are present. To illustrate, first samples can be obtained from a first group of subjects in which a first classification of cancer is present and second samples can be obtained from a second group of subjects in which a second classification of cancer is present. The sequencing data generated from the first samples can be analyzed by the computing system 214 to generate first metrics that correspond to classification regions for the first classification of cancer and the first metrics can be used to generate a first model that corresponds to the first classification of cancer. Additionally, the sequencing data generated from second samples can be analyzed by the computing system 214 to generate second metrics that correspond to classification regions for thefirst classification of cancer and the second metrics can be used to generate a second model that corresponds to the second classification of cancer. After the models have been trained, the computing system 214 can analyze sequencing data obtained from one or more additional subjects that were not included in the training subjects to determine classification region metrics for the one or more additional subjects. The classification region metrics can then be analyzed using the different tumor classification models to generate model outputs. The model outputs can be analyzed by the computing system to determine a model having greatest values for the respective model outputs and determine the tumor tissue classification that corresponds to the model.

[0210] In one or more additional illustrative implementations, the model output 230 can also indicate methylation status for one or more genomic regions of a reference sequence. For example, the computing system 214 can analyze the classification region metrics 226 to determine a methylation status of one or more promoter regions of a reference sequence. In various examples, the one or more promoter regions can include at least one promoter region that is related to the presence of a tumor in a subject. In one or more illustrative examples, the classification region metrics 226 can indicate a number of sequence representations having at least a threshold amount of methylation with respect to the one or more promoter regions. In these scenarios, the computing system 214 can determine that a promoter region is methylated in response to determining that the number of sequence representations having at least a threshold amount of molecules with a methylated cytosine in the promoter region is greater than a threshold number.

[0211] In still other illustrative implementations, the computing system 214 can analyze the sequencing data 212 to determine a quantitative measure that corresponds to a number of sequence representations that correspond to a promoter region and determine an additional quantitative measure that correspond to an additional number of sequence representations that correspond to a number of positive control regions. Normalized metrics can be determined based on the quantitative measure and the additional quantitative measure. The normalized metrics can be analyzed with respect to a threshold to determine a methylation status of the promoter region. In various examples, the threshold may be different for different promoter regions. The threshold can be determined using a cancer-free dataset and the threshold value is set such that falsepositive rates are no greater than 5%, no greater than 4%, no greater than 3%, no greater than 2%, or no greater than 1 % and at a specificity of at least 80%, at least 90%, at least 95%, at least 98%, or at least 99%. In at least some examples, the computing system 214 can analyze the promoter region with regard to the threshold in situations where at least 4 sequence representations correspond to the promoter region, where at least 5 sequence representations correspond to the promoter region, where at least 6 sequence representations correspond to the promoter region, where at least 7 sequence representations correspond to the promoter region, where at least 8 sequence representations correspond to the promoter region, where at least 9 sequence representations correspond to the promoter region, where at least 10 sequence representations correspond to the promoter region, where at least 11 sequence representations correspond to the promoter region, or where at least 12 sequence representations correspond to the promoter region.

[0212] In one or more further illustrative examples, the computing system 214 can combine results from multiple models to determine the model output 230. For example, the computing system 214 can execute models with respect to one or more epigenetic signals, such as methylation of classification regions, to determine one or more first tumor metrics. With regard to methylation, the computing system 214 can execute both a classification model, such as a logistic regression model, that produced an indication of cancer being present in a subject providing a sample and an additional model that predicts tumor fraction for a sample. In one or more examples, the epigenetic signals can also correspond to fragment lengths of sequence representations generated from samples. In addition, the computing system 214 can execute one or more additional models with respect to genomic signals to generate further tumor metrics with respect to samples. In various examples, the genomic signals can correspond to the presence of one or more single nucleotide variants (SNVs) and / or the presence of insertions or deletions at one or more genomic regions of a reference sequence. In at least some examples, the computing system can include an integration system that combines tumor metrics generated by executing a number of models with regard to data corresponding to the genomic signals and the epigenetic signals to produce an aggregated tumor metric for a given sample. In some embodiments, using the quantitative measure obtained from themodel output 230 can be analyzed with respect to a threshold. In situations where the quantitative measure obtained from the model output is at least the threshold value, the computing system 214 can determine that the indication of cancer is being present in the subject. In situations where the quantitative measure obtained from the model output is less than the threshold value, the computing system 214 can determine that the indication of cancer is being absent or not detected in the subject. In some embodiments, the threshold used to determine whether the indication of cancer is being present is calculated using a set of normal samples and is set at a particular value that provides high specificity.

[0213] In various additional implementations, the computing system 214 can determine methylation status of individual genomic regions. In one or more illustrative examples, the computing system 214 can determine methylation status of one or more promoter regions. In one or more examples, the sequencing data 212 can be analyzed to determine sequence representations that correspond to one or more genomic regions. For example, the sequencing data 212 can be analyzed to determine a number of sequence representations that correspond to one or more promoter regions. In at least some examples, the computing system 214 can determine a number of sequence representations that correspond to individual promoter regions that have at least a threshold amount of methylated cytosines.

[0214] For each genomic region and for an individual sample, the computing system 214 can determine a number of sequence representations that correspond to polynucleotide molecules having at least the threshold number of methylated cytosines in the genomic region. The computing system 214 can perform one or more normalization operations using the counts of polynucleotide molecules or sequence reads that correspond to the genomic region and have at least the threshold number of methylated cytosines to generate normalized metrics. To illustrate, the computing system 214 can divide the counts of polynucleotide molecules or reads that correspond to the genomic region and have at least the threshold number of methylated cytosines by the number of molecules or sequencing reads that correspond to a control region, such as a positive control region. In another instance, the computing system 214 can perform the normalized metrics by dividing the counts of polynucleotide molecules or reads thatcorrespond to the genomic region and have at least the threshold number of methylated cytosines by the number of molecules or sequencing reads in a control dataset (i.e., the control dataset comprises of tumor not-detected samples) corresponding to the same genomic region and have at least the same threshold number of methylated cytosines.

[0215] The normalized metrics can be analyzed with respect to a threshold value. The threshold value can correspond to a given genomic region, such as a given promoter region. In various examples, the threshold value can be different for different promoter regions. In these scenarios, a first promoter region can have a first threshold value and a second promoter region can have a second threshold value. In situations where the normalization metric is at least the threshold value, the computing system 214 can determine that the genomic region has a first methylation status. In scenarios where the normalization metric is less than the threshold value, the computing system 214 can determine that the genomic region has a second methylation status. In one or more illustrative examples, the first methylation status can be labeled as “methylated” and the second methylation status can be labeled as “not methylated.”

[0216] The threshold value for a given genomic region can be determined based on training data obtained from samples of individuals in which cancer is not detected. In one or more examples, sequence representations obtained from the training samples can be analyzed to determine a z-score with respect to the number of polynucleotide molecules that correspond to the genomic region and that have at least the threshold amount of methylated cytosines. In one or more illustrative examples, the threshold value for a promoter region that is used to determine the normalization metrics for the promoter region can be derived from the z-score calculated based on the training samples with respect to the promoter region.

[0217] Although the illustrative example of Figure 2 describes that models can be generated to determine a number of indicators with respect to the presence or absence of cancer in a given subject, in at least some additional examples, the sequencing data 212 can be analyzed by the computing system 214 to determine indicators of the presence of cancer without training specific models. In one or more examples, the computing system 214 can determine a tumor fraction value based on sequencing data 212 generated from one or more samples obtained from a single subject in which it isunknown whether or not cancer is present in the subject. In one or more examples, the computing system 214 can determine a change in the tumor fraction value based on sequencing data 212 generated from one or more samples obtained at two or more time points from a single subject. The change in the tumor fraction value can be used to monitor the subject’s response to treatment. In one or more additional examples, a first sample can be obtained from a subject prior to or at onset of at least one administration of a treatment or a procedure related to cancer and one or more second samples can be obtained from the subject after at least one of administration of a treatment or a procedure related to cancer. In one or more illustrative examples, the one or more second samples can be obtained at least one week, at least two weeks, at least three weeks, at least four weeks, at least five weeks, at least six weeks, at least eight weeks, or at least ten weeks after administration of the treatment or procedure. In at least some examples, first sample and the second sample can be derived from at least one of a bodily fluid obtained from the subject or tissue obtained from the subject.

[0218] In one or more examples, one or more samples can be obtained from a given subject. The sequencing data 212 generated from the one or more samples can be analyzed by the computing system to determine quantitative measures for a number of classification regions. In one or more examples, the quantitative measures can correspond to an amount of sequence representations that have at least a threshold amount of overlap with one or more classification regions. In one or more additional examples, the quantitative measures can correspond to sequence representations having at least a threshold amount of methylated cytosines in CpG regions having at least a threshold amount of CG content. In various examples, the indication of cancer being present in the subject can include tumor fraction. In one or more additional examples, the indication of cancer being present in the subject can include mutant allele fraction. In at least some examples, the quantitative measures can correspond to a number of sequencing reads that correspond to a given classification region in relation to a total number of sequencing reads across a plurality of positive control regions. In one or more further examples, the indicators of cancer being present can be used to determine an output that corresponds to cancer being present or not being present in a given individual in response to analyzing the one or more indicators of cancer being present with respectto one or more thresholds. In one or more illustrative examples, tumor fraction determined from one or more samples obtained from a subject can be analyzed with respect to one or more thresholds. In instances where tumor fraction is greater than a threshold level, the computing system 214 can determine that the probability of cancer being present in the subject is at least 80%, at least 85%, at least 90%, at least 95%, or at least 99%. Further, in situations where multiple samples are obtained from a subject, first quantitative measures generated from a first sample obtained from the subject can be analyzed with respect to second quantitative measures generated from a second sample obtained from the subject. In at least some examples, differences between the first quantitative measures and the second quantitative measures can be analyzed to determine an indication of treatment response in the subject.

[0219] The quantitative measures used to determine an indication of cancer being present in a subject can be determined by analyzing quantitative measures of a subset of classification regions. In at least some examples, the subset of classification regions can be different for different subjects. In one or more illustrative examples, values of quantitative measures for a number of classification regions can be analyzed with respect to one another and ranked according to the magnitude of the value of the quantitative measures. In various examples, the classification regions for a given sample can be ranked in descending order from the one or more classification regions having the greatest value of a quantitative measure to the one or more classification region having the least value of the quantitative measure.

[0220] In various examples, after ranking the quantitative measures of the classification regions, quantitative measures that correspond to a group of the classification regions can be removed before determining the indication of cancer being present in the subject. For example, the group of classification regions that are not used to determine the indication of cancer being present in the subject can include the 1 % of classification regions having the greatest quantitative measure values, the 2% of classification regions having the greatest quantitative measure values, 3% of classification regions having the greatest quantitative measure values, 4% of classification regions having the greatest quantitative measure values, 5% of classification regions having the greatest quantitative measure values, or the 6% ofclassification regions having the greatest quantitative measure values. In at least some examples, a number of classification regions having relatively high quantitative measure values can be excluded from the group of classification regions used to determine the indication of cancer being present in the subject because, in at least some cases, classification regions corresponding to quantitative measure values at or near the top of the ranked list can have non-tumor origins and / or be related to sequencing artifacts. Thus, by removing the quantitative measures that correspond to these classification regions from the analysis used to determine the indication of cancer being present in the subject, the accuracy with which the indication of cancer being present in the subject can increase.

[0221] In one or more examples, after determining the group of classification regions to be used to determine an indication of cancer being present in the subject, a subset of classification regions of the group can then be determined by identifying at least 10 classification regions of the group, at least 25 classification regions of the group, at least 50 classification regions of the group, at least 75 classification regions of the group, at least 100 classification regions of the group, at least 150 classification regions of the group, at least 200 classification regions of the group, at least 250 classification regions of the group, at least 300 classification regions of the group, at least 350 classification regions of the group, at least 400 classification regions of the group, at least 450 classification regions of the group, or at least 500 classification regions of the group having the greatest values for the respective quantitative measure.

[0222] In at least some examples, one or more statistical measures, such as at least one of mean, median, or mode, can be applied to the quantitative measures of the subset of the classification regions of the group to generate an initial indication of cancer being present in the subject. In various examples, the initial indication of cancer can be modified according to a scaling factor. The scaling factor can be applied to the initial indication of cancer being present in the subject because, in at least some scenarios, the positive control regions can have different amounts of methylated CpGs. For example, at least a portion of the positive control regions can have fully methylated CpGs while other positive control regions may not be fully methylated. Additionally, in various situations, some classification regions can correspond to a high value of an indication of cancer being present in subjects, such as 90% tumor fraction, 95% tumor fraction, 99% tumorfraction, or 100% tumor fraction, but nucleic acid molecules that correspond to these classification regions may not be fully methylated. To account for these cases, the scaling factor can be applied to the initial indication of cancer being present in the subject to provide a more accurate determination of the indication. In one or more illustrative examples, the scaling factor can be determined by analyzing indications of cancer being present in subjects determined using one or more techniques described herein in relation to additional data that corresponds to additional indications of cancer being present in subjects, such as validation data or other techniques that generate data orthogonal to the indications of tumors being present in subjects described herein.

[0223] In various examples, the classification regions used to determine the quantitative measures can correspond to classification regions that correspond to one or more portions of differentially methylated regions. In one or more examples, the differentially methylated regions can include promoter regions that correspond to one or more classifications of cancer. For example, the classification regions can be determined by analyzing a number of sequencing representations across a differentially methylated region. In these scenarios, one or more portions of the differentially methylated regions that overlap with at least at threshold number of sequencing representations can be included in the classification regions. In one or more examples, the quantitative measures of the one or more portions of the differentially methylated regions can be determined based on the molecule count distribution of the differentially methylated region. For example, the quantitative measures can be determined based on the molecule count within one or more peaks of the molecule distribution of the differentially methylated region. To illustrate, in various examples, the distribution of molecules across a differentially methylated region can indicate one or more peaks where greater amounts of molecules overlap with one or more subregions within the differentially methylated region. In various examples, the one or more genomic regions that correspond to the one or more subregions of the differentially methylated regions that correspond to the highest amounts of sequence representations for a sample can be defined as classification regions. In at least some examples, the distribution of sequence representations can have a peak that corresponds to a subregion of the differentially methylated region having a higher number of sequence representations than other subregions of the differentiallymethylated region. In these scenarios, the subregion can be identified as a classification region. By determining subregions of at least a portion of the differentially methylated regions used to determine the indication of cancer being present in the subject, the amount of computing resources and memory resources used to determine the indication of cancer being present in the subject can be decreased.

[0224] To illustrate, a classification region can include one or more portions of a differentially methylated region in which at least 50% of the sequencing representations obtained from a sample overlap, at least 55% of the sequencing representations obtained from a sample overlap, at least 60% of the sequencing representations obtained from a sample overlap, at least 65% of the sequencing representations obtained from a sample overlap, at least 70% of the sequencing representations obtained from a sample overlap, at least 75% of the sequencing representations obtained from a sample overlap, at least 80% of the sequencing representations obtained from a sample overlap, at least 85% of the sequencing representations obtained from a sample overlap, at least 90% of the sequencing representations obtained from a sample overlap, at least 95% of the sequencing representations obtained from a sample overlap, or at least 99% of the sequencing representations obtained from a sample overlap. In one or more illustrative examples, the one or more portions of the differentially methylated region that comprise a classification region can be contiguous with respect to a reference sequence.

[0225] In various examples, the computing system 214 can use a biological age of a subject in conjunction with the classification region metrics 226 to determine the model output 230. The biological age of a subject can be different from a chronological age of a subject. The chronological age of a subject can be measured from a date of birth of the subject. The biological age can correspond to a measure of health of the subject taking into account various biological conditions present in a subject, levels of various analytes present in a subject, physical characteristics of a subject, one or more combinations thereof, and the like.

[0226] The biological age of subjects can be determined using an additional computational model. The additional computational model can be trained using classification region metrics 226 derived from additional samples obtained from additional training subjects and the chronological age of the additional training subjects. In one ormore examples, the additional computational model can be trained using sequencing reads derived from the samples obtained from the additional training subjects. In various examples, the sequencing reads used to train the additional computational model can correspond to nucleic acid molecules derived from the additional samples that include CpG regions with at least a threshold amount of methylation. In one or more illustrative examples, the sequencing reads used to train the additional computational model can correspond to nucleic acid molecules derived from the additional samples that are included in a hypermethylation partition that corresponds to the one or more molecule separation processes 208. The determination of biological age by the computing system 214 using the additional computational model can be different from existing systems, methods, and techniques because methylation data derived from plasma samples can be used rather than the whole blood samples used to generate methylation data in existing systems, methods, and techniques. The implementations described herein can also be different from existing systems, methods, and techniques because quantitative measures determined by the additional computational model can be based on an analysis of genomic regions that correspond to a diagnostic assay for identifying subjects in which cancer is present. In existing systems, methods, and techniques the quantitative measures used to determine biological age can be based simply on an analysis of genomic regions that correspond to age-related conditions.

[0227] In at least some examples, a number of sequencing reads that correspond to a number of genomic regions can be analyzed by the additional computational model to determine a biological age of a subject. In various examples, quantitative measures of multiple genomic regions can be combined and then analyzed by one or more machine learning models to determine a biological of a subject. For example, k-nearest neighbors techniques can be applied to quantitative measures corresponding to number of sequencing reads corresponding to a number of genomic regions to generate modified quantitative measures. In one or more examples, the modified quantitative measures can correspond to additional genomic regions that include one or more portions of a plurality of genomic regions of a reference sequence. The modified quantitative measures can be provided as input to a regression machine learning model to determine the biological ageof a subject. In one or more illustrative examples, the regression machine learning model can include an Elastic Net machine learning model.

[0228] In one or more examples, the biological age of a subject can be a feature used in a computational model used to determine the model output 230. For example, subjects having a biological age that is greater than the chronological age of the subjects can have a higher likelihood of a tumor being present than subjects having a biological age that is similar to or less than the chronological age of the subjects. In one or more additional examples, the biological age of a subject can be used to determine responsiveness to one or more treatments for one or more types of cancer. In one or more illustrative examples, the biological age of subjects can correspond to one or more components of a machine learning model used to generate the model output 230. The one or more components of the machine learning model that correspond to biological age of subjects can have various weights.

[0229] Figure 3 is a diagrammatic representation of an example framework 300 to train a computational model 302 to determine one or more tumor metrics with respect to a sample, in accordance with one or more implementations. The framework 300 can include the computing system 214. The computing system 214 can execute the computational model 302 to generate one or more model outputs 304. In one or more examples, the computational model 302 can be a machine learning model. The model output 304 can include an indication corresponding to the presence or absence of a tumor in a subject that provided a sample. In one or more illustrative examples, the model output 304 can include a tumor fraction. In one or more additional illustrative examples, the model output 304 can include a probability of cancer being present in a subject. In one or more further illustrative examples, the model output can include an indication of cancer being present in a subject or an indication of cancer not being present in a subject. In still other illustrative examples, the model output 304 can indicate methylation status of one or more regions of nucleic acid molecules. To illustrate, the computing system 214 can execute the computational model 302 with respect to quantitative measures corresponding to a promoter region to determine an amount of methylation of the promoter region. In other illustrative examples, the model output 304 can include a tumor tissue indication of the sample.

[0230] The framework 300 can also include a sequence representation 306. In one or more examples, the sequence representation 306 can be generated based on analyzing nucleic acid molecules that are derived from a sample provided by a subject. The sequence representation 306 can include genomic regions having a number of nucleotides that correspond to a number of regions of interest. For example, the sequence representation 306 can include a sequence of nucleotides that corresponds to a first classification region 308. In addition, the sequence representation 306 can include a sequence of nucleotides that corresponds to a second classification region 310. Further, the sequence representation 306 can include a sequence of nucleotides that corresponds to a third classification region 312. In various examples, the first classification region 308, the second classification region 310, and the third classification region 312 of the sequence representation 306 can have differing amounts of methylated cytosines included in the respective classification regions 308, 310, 312. In one or more additional examples, the sequence representation 306 can include a sequence of nucleotides that corresponds to a positive control region 314 and a sequence of nucleotides that corresponds to a negative control region 316.

[0231] The computational model 302 can include a number of components that correspond to individual classification regions. In one or more examples, the components of the computational model 302 can have respective values that correspond to quantitative metrics of the respective classification regions. The quantitative metrics can indicate a number of sequence representations that correspond to the respective classification regions. In one or more examples, the computational model 302 can include a number of weights that are related to the respective components of the computational model 302. For example, the computational model 302 can include a first model component 318 that has a first weight 320. The first model component 318 can correspond to the first classification region 308. In addition, the computational model 302 can include a second model component 322 that has a second weight 324. The second model component 322 can correspond to the second classification region 310. In various examples, at least one of the first weight 320, the second weight 324, or the third weight 328 can be different from at least another one of the first weight 320, the second weight 324, or the third weight 328.

[0232] In one or more illustrative examples, a value for the first model component 318, the second model component 322, and the third model component 326 can be determined on a per sample basis. To illustrate, for different samples, the computational model 302 can determine different values for at least one of the first model component 318, the second model component 322, or the third model component 326. In various examples, the computing system 214 can determine first quantitative measures for the first classification region 308 based on sequencing data for a sample. The computing system 214 can execute the computational model 302 to determine a value for the first model component 318 based on the first quantitative measures. Additionally, the computing system 214 can determine second quantitative measures for the second classification region 310 based on sequencing data for the sample. The computing system 214 can execute the computational model 302 to determine a value for the second model component 322 based on the second quantitative measures. Further, the computing system 214 can determine third quantitative measures for the third classification region 312 based on sequencing data for the sample. The computing system 214 can execute the computational model 302 to determine a value for the third model component 326 based on the third quantitative measures. The first quantitative measures, the second quantitative measures, and the third quantitative measures can be determined based on numbers of sequence representations that have at least a threshold amount of methylation in CG regions that correspond to the first classification region 308, the second classification region 310, and the third classification region 312, respectively. In one or more additional illustrative examples, a value for the first weight 320, a value for the second weight 324, and a value for the third weight 328 can be determined on a per sample basis. For example, for different samples, the computational model 302 can determine different values for at least one of the first weight 320, the second weight 324, or the third weight 328.

[0233] In one or more examples, the computing system 214 can perform a training process to generate the computational model 302. In various examples, the training process can determine one or more features related to classification region metrics that can be used to determine the model output 304. Additionally, the training process can determine one or more parameters related to classification region metrics that can beused to determine the model output 304. For example, the training process can be used to determine the model components to include in the computational model 302 and the corresponding weights of the model components.

[0234] In the illustrative example of Figure 3, the training process can be performed using training data 330. The training data 330 can include information obtained with respect to at least a first group of subjects 332 and information obtained with respect to at least a second group of subjects 334. In one or more examples, the first group of subjects 332 can include subjects in which a tumor is not detected and the second group of subjects 334 can include subjects in which a tumor is detected. In various examples, the training data 330 can include characteristics related to amounts of methylation of classification regions of the reference sequence 306 for the first group of subjects 332 and the second group of subjects 334. For example, the training data 330 can indicate quantitative measures corresponding to numbers of sequence representations that have at least a threshold level of methylation for the classification regions 308, 310, 312 for the first group of subjects 332 and the second group of subjects 334. The training data 330 can also include weights for model components based on an analysis of sequencing data of the first group of subjects 332 and the second group of subjects 334. In one or more illustrative examples, the training data 330 can include values for the first weight 320, values for the second weight 324, and values for the third weight 328 based on classification region metrics determined from sequencing data obtained from samples provided by the first group of subjects 332 and the second group of subjects 334.

[0235] The training data 330 can also include information corresponding to additional characteristics of the first group of subjects 332 and the second group of subjects 334. To illustrate, the training data 330 can include medical records information, medical history information, cancer treatment history information, demographic information, genomics information, one or more combinations thereof, and the like.

[0236] In one or more examples, the computing system 214 can train the computational model 302 to determine an indication related to one or more types of cancer being present in an individual. Additionally, in various examples, the computational model 302 can comprise multiple different models, such that the computational model 302 is an ensemble model. In these situations, the computing system 214 can performone or more training processes with respect to individual models of the ensemble model. In one or more illustrative examples, the computational model 302 can include a number of individual models that each correspond to determining model outputs for individual genomic regions, such as genes or for a specified group of genes. For example, the computational model 302 can include a number of individual models to generate maximum MAF values for individual genes or for a specified group of genes. In these scenarios, the training of the computational model 302 can have more constraints than other models used to determine indications of cancer being present in individuals because of the use of genomic information in the training process. As a result, in situations where the computational model 302 is training using genomic information, the accuracy of the output of the computational model 302 can be increased. Further, although the training of the computational model 302 can incorporate genomic information to determine maximum MAF values, the use of the computational model 302 to determine indications of cancer for test subjects after training can be performed without the use of genomic information and can be based on input vectors that correspond to quantitative measures determined from sequencing data obtained from the test subjects.

[0237] The computing system 214 can obtain a first training dataset 336 up to an Nth training dataset 338 to perform a training process to generate the computational model 302. In one or more examples, the first training dataset 336 can include a first portion of the training data 330 corresponding to the first group of subjects 332 and the second group of subjects 334 that is used to train the computational model 302 and the Nth training dataset 338 can include a second portion of the training data 330 corresponding to the first group of subjects 332 and the second group of subjects 334 as part of a validation process for the computational model 302. In various examples, the computational model 302 can be updated over time and undergo multiple training processes. In these scenarios, the first training dataset 336 can include a portion of the training data 330 for the first group of subjects 332 and the second group of subjects 334 that corresponds to a first period of time and the Nth training dataset 338 can include a portion of the training data 330 for the first group of subjects 332 and the second group of subjects 334 that corresponds to a second period of time.

[0238] In one or more examples, during the training process for the computational model 302, the computing system 214 can perform one or more optimization operations. In one or more illustrative examples, the computing system 214 can identify, during the training process for the computational model 302, one or more samples obtained from at least one of the first group of subjects 332 or the second group of subjects 334 that are outliers with respect to samples obtained from other subjects included in at least one of the first group of subjects 332 or the second group of subjects 334. To illustrate, the computing system 214 can determine that model output 304 generated for one or more subjects included in at least one of the first group of subjects 332 or the second group of subjects 334 has at least a threshold amount of difference with the model output 304 generated for one or more additional subjects included in at least one of the first group of subjects 332 or the second group of subjects 334. In one or more examples, the computing system 214 can identify at least one of one or more first subjects 332 or one or more second subjects 334 have model output 304 that is at least one standard deviation, at least 1.5 standard deviations, at least 2 standard deviations, at least 2.5 standard deviations, or at least 3 standard deviations different from a mean model output 304 determined for an additional group of at least one of the first group of subjects 332 or the second group of subjects 334. In various examples, the computing system 214 can apply a penalty to information generated from samples that correspond to subjects that are outliers with respect to information generated from samples that correspond to additional subjects.

[0239] In one or more additional examples, one or more optimization processes implemented by the computing system 214 in the training of the computational model 302 can correspond to a number of training cycles and / or a number of iterations for individual training cycles that are performed during the training process.

[0240] In one or more illustrative examples, the computing system 214 can perform at least 1000 iterations of a training process to generate the computational model 302, at least 3000 iterations of a training process to generate the computational model 302, at least 5000 iterations of a training process to generate the computational model 302, at least 8000 iterations of a training process to generate the computational model 302, at least 10,000 iterations of a training process to generate the computational model 302, atleast 12,000 iterations of a training process to generate the computational model 302, or at least 15,000 iterations of a training process to generate the computational model 302. In various examples, the computing system 214 can end the training process before convergence of a loss function related to the computational model 302. In one or more examples, the number of iterations of the training process to produce the computation model 302 can correspond to a number of iterations of the training process performed before the training process is stopped and before the convergence of the loss function.

[0241] In one or more examples, a first stage of the training process implemented by the computing system 214 to generate the computational model 302 can include determining samples included in the training data 330 that include somatic mutations indicative one or more types of cancer in relation to samples included in the training data 330 that do not include somatic mutations indicative of the one or more types of cancer. The computing system 214 can then performing a training process for the computational model 302 using the samples of the training data 330 that include one or more somatic mutations indicative of the one or more types of cancer and using a number of samples obtained from subjects in which a tumor is not detected. In various examples, at least 100 iterations of the first stage of the training process can be performed.

[0242] Further, the training process performed by the computing system 214 can include a second stage that includes predicting values of tumor metrics of samples that do not include somatic mutations with respect to the one or more types of cancer. The computing system 214 can the perform at least 100 additional iterations of the second stage of the training process to generate the computational model 302. The second stage of the training process performed by the computing system 214 to generate the computational model 302 can also include training the computational model 302 using portions of the training data 330 corresponding to samples having somatic mutations indicative of the one or more types of cancer, using the predicted values of sample that do not include somatic mutations indicative of the one or more types of cancer, and portions of the training data 330 that correspond to samples obtained from subjects in which a tumor is not detected. In various examples, the second stage of the training process performed by the computing system 214 to generate the computational model 302 can be performed at least 2 additional times, at least 3 additional times, at least 4additional times, at least 5 additional times, or at least 6 additional times. After the first stage of the training process and the second stage of the training process have been completed, the computing system 214 can perform a validation process for the computational model 302 using information obtained from different samples included in the training data 330.

[0243] In one or more illustrative examples, the computing system 214 can perform a training process for multiple computational models 302. In these scenarios, individual computational models 302 trained by the computing system 214 can correspond to different tissue types that are sources of genomic material obtained from subjects included in the training data 330. In one or more examples, the individual computational models 302 trained by the computing system 214 can correspond to different classification of cancer, such as colorectal cancer, lung cancer, pancreatic cancer, bladder cancer, breast cancer, liver cancer, skin cancer, or one or more additional classifications of cancer. In situations where the computing system 214 trains multiple computational models 302 that correspond to different classifications of cancer, the output from individual computational models 302 can be aggregated and analyzed by the computational system 214 to determine a tissue of origin for a subject.

[0244] In various examples, the individual computational models 302 that correspond to a given tissue from which genomic material included in samples is derived can have different model components. For example, a first computational model generated by the computing system 214 that corresponds to a first tissue type can have first model components that correspond to a first set of classification regions. In addition, a second computational model generated by the computing system 214 that corresponds to a second tissue type can have second model components that correspond to a second set of classification regions that has at least one classification region different from the first set of classification regions. Additionally, the weights for the individual components of the computational models that correspond to different tissue types can be different. That is, in situations where the first set of classification regions of the first computational model and the second set of classification regions of the second computational model have at least one classification region in common, the weights for the model componentthat corresponds to the at least one common classification region can be different in relation to the first computational model and the second computational model.

[0245] Additionally, one or more additional normalization processes can be performed by the computing system when generating the computational model 302. For example, in at least some scenarios, molecules treated with MBD can be partitioned differently across different samples. In one or more examples, molecules can be partitioned differently across different samples due to differences in the composition of reagents used to treat the molecules with MBD. In one or more additional examples, molecules can be partitioned differently across different samples due to at least one of equipment differences or process conditions used to treat the molecules with MBD.

[0246] To illustrate, for one or more first samples, treatment with MBD can cause first molecules having regions with first CG content to be separated into a first partition and second molecules having regions with second CG content to be separate into a second partition. In addition, for one or more second samples, treatment with MBD can cause third molecules having third CG content that is different from the first CG content to be separated into the first partition and fourth molecules having regions with fourth CG content that is different from the second CG content to be separated into the second partition. In various examples, the first molecules can be treated with MBD and separated into the first partition and the second molecules can be treated with MBD and separated into the second partition across a first cutoff range of CG content. Further, the third molecules can be treated with MBD and separated into the first partition and the fourth molecules can be treated with MBD and separated into the second partition across a second cutoff range of CG content that is different from the first cutoff range.

[0247] In one or more illustrative examples, the first cutoff range of CG content can include from 3-10 CpGs having methylated cytosines and the second cutoff range can include from 6-14 CpGs having methylated cytosines. In one or more additional illustrative examples, the first cutoff range of CG content can include from 4-9 CpGs having methylated cytosines and the second cutoff range can include from 7-13 CpGs having methylated cytosines. In one or more further illustrative examples, the first cutoff range of CG content can include from 5-8 CpGs having methylated cytosines and the second cutoff range can include from 8-12 CpGs. In still other illustrative examples, the first cutoffrange of CG content can include 4-7 CpGs and the second cutoff range can include from 6-10 CpGs. In various examples, the first cutoff range of CG content and the second cutoff range of CG content can be used to determine the threshold amount of methylated cytosines used to determine at least one of training sequencing reads or testing sequencing reads. In at least some examples, the threshold amount of methylated cytosines can include a cutoff number that corresponds to a probability, such as at least about 80%, at least about 85%, at least about 90%, at least about 95%, or at least about 99% of individual molecules treated with MBD being separated into a given partition. In one or more examples, the threshold amount of methylated cytosines can correspond to 5 methylated cytosines, 6 methylated cytosines, 7 methylated cytosines, 8 methylated cytosines, 9 methylated cytosines, 10 methylated cytosines, 11 methylated cytosines, 12 methylated cytosines, 13 methylated cytosines, or 14 methylated cytosines.

[0248] In one or more examples, the computing system 214 can generate metrics for individual classification regions based on quantitative measures that are determined by analyzing a first number of sequencing reads to identify a first number of nucleic acid molecules having a first amount of CG content and by analyzing a second number of sequencing reads to identify a second number of nucleic acid molecules having a second amount of CG content. In at least some examples, the second number of nucleic acid molecules can be used to modify a metric determined using the first number of nucleic acid molecules to account for variations in the separation of molecules treated using MBD for different samples. In various examples, for individual classification regions, a first metric can be determined for a given sample by determining a first quantitative measure that corresponds to a number of molecules having a threshold amount of methylated cytosines and having a first amount of cytosine-guanine content in one or more partitions (for example, second partition 130 and / or third partition 134) that correspond to the individual classification region. In some embodiments, the first amount of CG content can be at least 5, at least 6, at least 7, at least 8, at least 9, at least 10, at least 15, at least 20, at least 25, or at least 30 CpGs in the nucleic acid molecules. In some embodiment, the first amount of CG content can be between 5-10, 5-15, 5-20, 5-30, 10-15, 10-20, IQ- 30, 15-20, 15-30 or 20-40 CpGs in the nucleic acid molecules.

[0249] The first metric can also be determined for a given sample by determining a second quantitative measure that corresponds to a number of molecules having a threshold amount of methylated cytosines and having the first amount of cytosine-guanine content in one or more partitions (for example, second partition 130 and / or third partition 134) that correspond to a plurality of control regions (e.g., positive control regions). To illustrate, for an individual classification region, the first metric can be determined using the first quantitative measure for the individual classification region and the second quantitative measure that corresponds to the plurality of control regions.

[0250] The normalization process can also include determining, for a given sample, a second metric for the given sample by determining one or more additional quantitative measures based on a number of molecules in one or more partitions (e.g., second partition 130 and / or third partition 134) having at least the threshold amount of methylated cytosines and a second amount of cytosine-guanine content that correspond to the plurality of control regions, where the second amount of cytosine-guanine content is less than the first amount of cytosine-guanine content. In some embodiments, the second amount of CG content can be between 5-10, 5-15, 10-15, 10-20 or 15-20 CpGs in the nucleic acid molecules. In one or more examples, the plurality of control regions can be positive control regions and / or negative control regions. In one or more examples, the second metric can be determined using the additional quantitative measure and the second quantitative measure. In at least some examples, the second metric can be determined for a given sample by determining a ratio of the one or more additional quantitative measures with respect to the second quantitative measure. In one or more additional examples, the second metric can be determined for a given sample by determining the logarithm, such as the logarithm according to base 10, of a ratio of the one or more additional quantitative measures with respect to the second quantitative measure.

[0251] In one or more illustrative examples, the second metric for a given sample can include a combination of values, where individual values correspond to an additional quantitative measure based on a number of molecules having at least a threshold amount of methylated cytosines and a given number of CpGs for the plurality of control regions and the second quantitative measure. For example, a first additional quantitative measurecan be determined based on a first number of molecules having at least the threshold amount of methylated cytosines in control regions having a first number of CpGs, such as 6, and a second additional quantitative measure can be determined based on a second number of molecules having at least the threshold amount of methylated cytosines in control regions having a second number of CpGs, such as 7. In at least some examples, more additional quantitative measures can be determined based on additional numbers of molecules having the threshold amount of methylated cytosines in control regions having additional numbers of CpGs, such as 8 CpGs, 9, CpGs, 10 CpGs, and the like up to an upper threshold of CpGs, such as 12 CpGs, 13 CpGs, or 14 CpGs. Ratios determined using the additional quantitative measures with respect to the second quantitative measures can be determined and summed to determine the second metric.

[0252] In various examples, a correlation factor can also be determined for individual classification regions in relation to different amounts of CpGs that can be used to determine the second metric. In one or more examples, the correlation factor can modify the individual additional quantitative measures and then the modified individual additional quantitative measures can be aggregated to determine the second metric. In one or more additional examples, the first metric and the second metric can be combined to determine a normalized metric that corresponds to a given classification region. In one or more illustrative examples, the second metric can be subtracted from the first metric to determine the normalized metric.

[0253] In one or more additional illustrative examples, the correlation factor for a given classification region can be determined for each of a plurality of different amounts of cytosine-guanine content, such as a first correlation factor for 6 CpGs, a second correlation factor for 7 CpGs, a third correlation factor for 8 CpGs, and so forth up to a threshold amount of CG content. In at least some examples, the correlation factor can be determined by analyzing training data using one or more linear regression techniques. For example, the training data 330 can be fit to a linear regression model for individual classification regions to determine the correlation factor. In various examples, the fitting of at least a portion of the training data 330 to the linear regression model can be performed by aggregating the additional quantitative measures for a given classificationregion across a range of CG content, such a 6 CpGs, 7 CpGs, up to a threshold number of CpGs, and determining a mean quantitative measure.

[0254] In one or more examples, the normalized metrics can reduce variation of quantitative measures determined for individual samples. In at least some examples, the reduction in variation can result in increased accuracy of model outputs 304 in relation to at least some model outputs 304 determined without implementing the additional normalization process to determine the normalized metric.

[0255] Figure 4 is a diagrammatic representation of a framework 400 for generating training data for use in training a computational model that determines indications of cancer being present in subjects, in accordance with one or more example implementations. In the framework 400, a plurality of subjects 402 can provide a plurality of samples 404. In one or more examples, at least a portion of the plurality of samples 404 can include biological fluid samples. In one or more illustrative examples, the plurality of samples 404 can be selected from one or more of blood, plasma, serum, urine, fecal, saliva samples, whole blood, a blood fraction, pleural fluid, pericardial fluid, cerebrospinal fluid, peritoneal fluid, one or more combinations thereof, and the like. In addition, the plurality of samples 404 can include tissue samples. For example, at least a portion of the plurality of samples 404 can be obtained from a tissue biopsy. In various examples, the plurality of subjects 402 can include subjects in which a tumor has been detected.

[0256] Additionally, nucleic acid molecules can be extracted from the plurality of samples 404. In at least some examples individual samples of the plurality of samples 404 can comprise an amount of cell-free nucleic acid molecules. The extraction of nucleic acid molecules from the plurality of samples 404 can include implementing one or more cell lysis techniques to cleave the membranes of cells included in the plurality of samples 404 and applying one or more proteases to break down proteins included in the plurality of samples 404. The extraction of nucleic acid molecules from the plurality of samples 404 can also include a number of washing and / or elution techniques to separate the nucleic acid molecules from other components included in the plurality of samples 404. In various examples, thousands, up to millions, up to billions of nucleic acid molecules can be extracted from individual samples of the plurality of samples 404.

[0257] The framework 400 can also include one or more molecule separation and sequencing processes 406 that are performed with respect to the plurality of samples 404. The one or more molecule separation and sequencing processes 406 can correspond to separating nucleic acid molecules into a number of partitions based on the characteristics of the nucleic acid molecules. Examples of characteristics that can be used for partitioning nucleic acid molecules include multiple different nucleotide modifications, methylation level, nucleosome binding, sequence mismatch, immunoprecipitation, and / or proteins that bind to DNA. In one or more illustrative examples, a heterogeneous population of nucleic acid molecules can be partitioned into nucleic acid molecules with one or more epigenetic modifications and without the one or more epigenetic modifications. Examples of epigenetic modifications include, but are not limited to, presence or absence of methylation; level of methylation, hydroxymethylation, and type of methylation (5' cytosine or 6 methyladenine).

[0258] The nucleic acid molecules extracted from plurality of samples 404 can include molecules having varying levels of methylation. Methylation can occur from any one or more post-replication or transcriptional modifications. Post-replication modifications include modifications of the nucleotide cytosine, including, but not limited to, 5-methylcytosine, 5-hydroxymethylcytosine, 5-formylcytosine and 5-carboxylcytosine. The one or more molecule separation and sequencing processes 406 can separate nucleic acid molecules extracted from plurality of samples 404 into a number of partitions with individual partitions corresponding to different levels of methylation. For example, the molecule separation and processes 406 can produce a first partition of nucleic acid molecules having first levels of methylation, a second partition of nucleic acid molecules having second levels of methylation, and a third partition of nucleic acid molecules having third levels of methylation. In various examples, the second levels of methylation can be greater than the first levels of methylation and the third levels of methylation can be greater than the first levels of methylation and the second levels of methylation. In one or more illustrative examples, the molecule separation proceeds of the one or more molecule separation and sequencing processes 406 can include the first molecule separation process 122 and the second molecule separation process 136 described with respect to Figure 1.

[0259] The sequencing processes included in the molecule separation and sequencing processes 406 can be performed by one or more sequencing machines that produce positive sample sequencing data 408. In one or more examples, the positive sample sequencing data 408 can include sequencing reads that correspond to nucleic acid molecules derived from the plurality of samples 404 having at least threshold levels of methylation. In one or more illustrative examples, positive sample sequencing data 408 can include sequencing reads corresponding to nucleic acid molecules having at least a threshold amount of methylation in CG regions of the nucleic acid molecules. In one or more additional illustrative examples. The positive sample sequencing data 408 can include sequencing reads corresponding to nucleic acid molecules that are hypermethylated.

[0260] The framework 400 can also include a computing system 410. The computing system 410 can obtain the positive sample sequencing data 408 and then analyze the positive sample sequencing data 408 to determine subsets of nucleic acid molecules that are to be used in training a classification model that can determine metrics indicating the presence of cancer or not in a subject. The computing system 410 can include one or more computing devices that can include at least one of one or more desktop computing devices, one or more mobile computing devices, or one or more server computing device. In various examples, at least a portion of the one or more computing devices implementing the computing system 410 can be included in a remote computing environment, such as a cloud computing environment. In one or more examples, the computing system 410 and the equipment used to perform the molecule separation and sequencing processes 406 can be implemented owned, operated, maintained, and / or controlled by a single organization. In one or more additional examples, the computing system 410 and the molecule separation and the equipment used to perform the sequencing processes 406 can be implemented, owned, operated, maintained, and / or controlled by multiple organizations. In one or more illustrative examples, the sequencing operations included in the molecule separation and sequencing processes 406 can include the operations performed by the sequencing machine 140 described with respect to Figure 1 and the sequencing machine 202 described with respect to Figure 2.

[0261] The computing system 410 can include a first computational model 412. In one or more examples, the first computational model 412 can include a classification model that implements one or more machine learning techniques. In one or more additional examples, the first computational model 412 can include a linear regression model. In one or more illustrative examples, the first computational model 412 can include one or more implementations of the computational model 302 described with respect to Figure 3. In one or more scenarios, the first computational model 412 can be trained using sequencing data derived from samples obtained from individuals in which cancer is present and individuals in which cancer is not present. In various examples, the first computational model 412 can analyze the positive sample sequencing data 408 to determine a model output indicating an indication of cancer for individual samples of the plurality of samples 404. In at least some examples, the first computational model 412 can analyze, for individual samples of the plurality of samples 404, a number of sequencing reads included in the positive sample sequencing data 408 corresponding to individual classification regions. In one or more implementations, the first computational model 412 can, for individual samples of the plurality of samples 404, determine quantitative measures for individual classification regions based on the number of sequencing reads included in the positive sample sequencing data 408 that correspond to the individual classification regions. The first computational model 412 can determine a sample quantitative measure 414 for individual samples of the plurality of samples 404 according to the individual quantitative measures for the individual classification regions. The sample quantitative measures 414 can correspond to an indication of cancer being present in individual subjects of the plurality of subjects 402. In one or more additional illustrative examples, the first computational model 412 can analyze the positive sample sequencing reads 408 to determine sample quantitative measures 414 that include mutant allele fractions for individual samples of the plurality of samples 404. In one or more further examples, the first computational model 412 can analyze the positive sample sequencing reads 408 to determine sample quantitative measures 414 that include tumor fractions for individual samples of the plurality of samples 404.

[0262] The computing system 410 can include a training data analysis system 416 that analyzes the sample quantitative measures 414 in relation to a number of analysiscriteria. The computing system 410 can apply a number of analysis criteria to the sample quantitative measures 414 to determine a number of sets of training samples to train a computational model that is different from the first computational model 412. In one or more examples, the training data analysis system 416 can apply first analysis criteria 418 to the sample quantitative measures 414. The first analysis criteria 418 can indicate one or more ranges of values for the sample quantitative measures 414. The one or more ranges of values for the sample quantitative measures 414 can be determined through a number of experiments to determine an optimal range of values for the sample quantitative measures 414 for training of the additional computational model. In various examples, the training data analysis system 416 can apply the first analysis criteria 418 to the sample quantitative measures 414 to produce first training samples 418.

[0263] In one or more examples, the computing system 410 can determine the first training samples 418 by analyzing the individual values for the sample quantitative measures 414 to determine whether or not the values are within the range indicated by the first analysis criteria 418. In situations where the value for an individual sample quantitative measure 414 is within a range of values indicated by the first analysis criteria 418, training data analysis system 416 can add the individual sample quantitative measure 414 to the first training samples 418. In scenarios where the value for an individual sample quantitative measure 414 is outside of the range of values indicated by the first analysis criteria 418, the training data analysis system 416 can add the individual sample quantitative measure 414 to a set of residual training samples (not shown in Figure 4). In at least some examples, the residual training samples can be used to generate in silico samples that can be used to train one or more additional computational models.

[0264] In one or more illustrative examples, the first analysis criteria 418 can correspond to a range of mutant allele fraction values for the sample quantitative measures 414. In one or more implementations, the mutant allele fraction values can be expressed as percentage values. In one or more additional examples, individual sample quantitative measures 414 can include values for tumor fraction of individual samples of the plurality of samples 404. In one or more further examples, individual sample quantitative measures 414 can include values for fragment length distributions forindividual samples of the plurality of samples 404. In still other examples, individual sample quantitative measures 414 can include values of one or more protein biomarker concentrations in individual samples of the plurality of samples 404. The individual sample quantitative measures 414 can also include values indicating B-cell concentrations in individual samples of the plurality of samples 404. Additionally, the individual sample quantitative measures 414 can include values indicating T-cell concentrations in individual samples of the plurality of samples 414. Further, the individual sample quantitative measures 414 can include values indicating ratios of B-cell concentrations to T-cell concentrations for individual samples of the plurality of samples 414.

[0265] In at least some examples, the first analysis criteria 418 can correspond to a range of mutant allele fraction values based on one or more types of cancer to be detected. For example, the first analysis criteria 418 can correspond to a first range of mutant allele fraction values in situations where a first type of cancer is being detected and the first analysis criteria 418 can correspond to a second range of mutant allele fraction values in situations where a second type of cancer is being detected. In still other example, the first analysis criteria 418 can correspond to a first range of mutant allele fraction values in situations where one or more first stages of cancer are being detected and a second range of mutant allele fraction values in situations where one or more second stages of cancer are being detected. The second range of mutant allele fraction values can be different from the first range of mutant allele fraction values. In at least some examples, the second range of mutant allele fraction values can partially overlap with the first range of mutant allele fraction values. In various examples, the second range of mutant allele fraction values may not overlap with the first range of mutant allele fraction values.

[0266] In one or more additional illustrative examples, the first analysis criteria 418 can indicate a range of mutant allele fraction values that correspond to no greater than 50% of the sample quantitative measures 414, no greater than 40% of the sample quantitative measures 414, no greater than 30% of the sample quantitative measures 414, no greater than 20% of the sample quantitative measures 414, no greater than 15% of the sample quantitative measures, no greater than 10% of the sample quantitative measures 414, or no greater than 5% of the sample quantitative measures 414. In variousillustrative examples, the first analysis criteria 414 can indicate a range of mutant allele fraction values from 1% of the sample quantitative measures 414 to 50% of the sample quantitative measures 414, from 5% of the sample quantitative measures 414 to 40% of the sample quantitative measures 414, from 10% of the sample quantitative measures 414 to 30% of the sample quantitative measures 414, from 1% of the sample quantitative measures 414 to 10% of the sample quantitative measures 414, or from 5% of the sample quantitative measures 414 to 15% of the sample quantitative measures 414.

[0267] In one or more further illustrative examples, the first analysis criteria 418 can indicate mutant allele fraction values for the sample quantitative measures 414 of no greater than 0.001%, no greater than 0.005%, no greater than 0.008%, no greater than 0.01 %, no greater than 0.03%, no greater than 0.05%, no greater than 0.08%, no greater than 0.1 %, no greater than 0.3%, no greater than 0.5%, no greater than 0.8%, no greater than 1.0%, no greater than 1.5%, no greater than 2%, no greater than 3%, no greater than 5%, no greater than 8%, or no greater than 10%. In various examples, the first analysis criteria 418 can indicate mutant allele fraction values for the sample quantitative measures 414 from 0.001 % to 10%, from 0.005% to 1 %, from 0.01 % to 1%, from 0.01% to 0.1%, from 0.05% to 5%, or from 0.1 % to 1 %.

[0268] The training data analysis system 416 can also apply second analysis criteria 420 to the first training samples 418 to produce second training samples 422 and third training samples 424. In one or more examples, the second analysis criteria 420 can correspond to the presence of somatic mutations present in nucleic acid molecules derived from the plurality of samples 404. For example, the second training samples 422 can include a first subset of the first training samples 418 in which at least a threshold number of somatic variants are present. Additionally, the third training samples 424 can include a second subset of the first training samples 418 in which less than the threshold number of somatic mutations are present. In one or more illustrative examples, the second subset of the first training samples 418 can correspond to nucleic acid sequences in which no somatic mutations are present.

[0269] In various examples, the training data analysis system 416 can analyze the first training samples 418 with respect to the second analysis criteria 420 by analyzing nucleic acid sequences included in the positive sample sequencing data 408 thatcorrespond to the first training samples 418 with respect to one or more reference sequences. In at least some examples, the training data analysis system 416 can analyze nucleotides of individual positions of nucleic acid molecules included in the positive sample sequencing data 408 that correspond to the first training samples 418 with nucleotides present at individual positions of the one or more reference sequences. The training data analysis system 416 can determine that one or more somatic mutations are present in a first training sample 418 in response to determining that a nucleic acid sequence corresponding to the first training sample 418 has a first nucleotide present at a given position that is different from a second nucleotide present at the given position of at least one reference sequence. In one or more additional examples, the second analysis criteria 420 can include a list of somatic mutations. In these scenarios, the training data analysis system 416 can analyze nucleic acid molecule sequences included in the positive sample sequencing data 408 that correspond to the first training samples 418 with respect to the list of somatic mutations. For a first subset of the first training samples 418 in which a corresponding nucleic acid molecule sequence includes one or more somatic mutations included in the list of somatic mutations, the training data analysis system 416 can add the first subset of first training samples 418 to the second training samples 422. For a second subset of the first training samples 418 in which a corresponding nucleic acid molecule sequence does not include one or more somatic mutations included in the list of somatic mutations, the training data analysis system 416 can add the second subject of first training samples 418 to the third training samples 422.

[0270] The computing system 410 can perform a training process 426 for a second computational model 428 using the second training samples 422 and the third training samples 424. In one or more examples, additional datasets can be used in the training process 426. For example, the computing system 410 can perform the training process 426 for the second computational model 428 using at least one of methylation data or sequencing data derived from samples obtained from subjects in which a tumor is not detected. In one or more additional examples, the computing system 410 can perform the training process 426 for the second computational model 428 using at least one of methylation data or sequencing data that correspond to in silico samples derived from the at least one of methylation data or sequencing data combine from a plurality of additionalsamples. In one or more illustrative examples, the second computational model 428 can include a classification model. In one or more additional illustrative examples, the second computational model 428 can include a regression model. The regression model can comprise a linear regression model. Additionally, the regression model can comprise a logistic regression model. Further, the regression model can comprise a ridge regression model. In still other examples, the regression model can comprise a lasso regression model. The regression model can also include a polynomial regression model.

[0271] In one or more examples, the training process 426 can be performed with respect to a loss function of the second computational model 428. In one or more illustrative examples, the loss function can comprise a Huber loss function. In one or more additional illustrative examples, the loss function of the second computational model 428 can comprise a support vector regression loss function. In one or more further illustrative examples, the loss function of the second computational model 428 can comprise a ridge loss function. In various illustrative examples, the loss function of the second computational model 428 can comprise a lasso loss function. In still other illustrative examples, the loss function of the second computational model 428 can comprise an elastic net loss function. The loss function of the second computational model 428 can also include a square error loss function.

[0272] The second computational model 428 can generate a model output that corresponds to an indication of cancer being present in one or more subjects. In one or more examples, an output of the second computational model 428 can indicate if a tumor is detected in one or more subjects or if a tumor is not detected in one or more subjects. In one or more additional examples, an output of the second computational model 428 can correspond to values for tumor fraction for one or more subjects. In one or more further examples, an output of the second computational model 428 can include values indicating a probability of a tumor being present in one or more subjects. In still other examples, an output of the second computational model 428 can indicate a stage of cancer present in one or more subjects. In at least some examples, an output of the second computational model 428 can indicate a type of tissue in which a tumor is present in one or more subjects. In various examples, an output of the second computational model 428 can include an indication of a type of tissue in which a tumor is present in theone or more subjects as well as at least one of one or more values for tumor fraction, a stage of cancer, or a probability of a tumor being present in one or more subjects.

[0273] Using a portion of the sample quantitative measures 414 for training of the second computational model 428 as described herein can result in fewer processing resources and fewer memory resources being used to determine a trained version of the second computational model 428 than in scenarios where all or almost all of the sample quantitative measures 414 are used to train the second computational model 428. Additionally, by training the second computational model 428 using data derived from a specifically selected subset the plurality of training samples 404, the second computational model 428 can produce output that is more accurate and reliable than if data derived from all or almost all of the plurality of samples 404 was used.

[0274] Figure 5 is a diagrammatic representation of a framework 500 of a training process for a computational model that produces indications of cancer being present in one or more subjects, in accordance with one or more example implementations. In the framework 500, a plurality of subjects 502 can provide a plurality of samples 504. In one or more examples, at least a portion of the plurality of samples 504 can include biological fluid samples. In one or more illustrative examples, the plurality of samples 504 can be selected from one or more of blood, plasma, serum, urine, fecal, saliva samples, whole blood, a blood fraction, pleural fluid, pericardial fluid, cerebrospinal fluid, peritoneal fluid, one or more combinations thereof, and the like. In addition, the plurality of samples 504 can include tissue samples. For example, at least a portion of the plurality of samples 504 can be obtained from a tissue biopsy. In various examples, the plurality of subjects 502 can include subjects in which a tumor has not been detected.

[0275] Additionally, nucleic acid molecules can be extracted from the plurality of samples 504. In at least some examples individual samples of the plurality of samples 504 can comprise an amount of cell-free nucleic acid molecules. The extraction of nucleic acid molecules from the plurality of samples 504 can include implementing one or more cell lysis techniques to cleave the membranes of cells included in the plurality of samples 504 and applying one or more proteases to break down proteins included in the plurality of samples 504. The extraction of nucleic acid molecules from the plurality of samples 504 can also include a number of washing and / or elution techniques to separate thenucleic acid molecules from other components included in the plurality of samples 504. In various examples, thousands, up to millions, up to billions of nucleic acid molecules can be extracted from individual samples of the plurality of samples 504.

[0276] The framework 500 can also include one or more molecule separation and sequencing processes 506 that are performed with respect to the plurality of samples 504. The one or more molecule separation and sequencing processes 506 can correspond to separating nucleic acid molecules into a number of partitions based on the characteristics of the nucleic acid molecules. Examples of characteristics that can be used for partitioning nucleic acid molecules include multiple different nucleotide modifications, methylation level, nucleosome binding, sequence mismatch, immunoprecipitation, and / or proteins that bind to DNA. In one or more illustrative examples, a heterogeneous population of nucleic acid molecules can be partitioned into nucleic acid molecules with one or more epigenetic modifications and without the one or more epigenetic modifications. Examples of epigenetic modifications include, but are not limited to, presence or absence of methylation; level of methylation, hydroxymethylation, and type of methylation (5' cytosine or 6 methyladenine).

[0277] The nucleic acid molecules extracted from plurality of samples 504 can include molecules having varying levels of methylation. Methylation can occur from any one or more post-replication or transcriptional modifications. Post-replication modifications include modifications of the nucleotide cytosine, including, but not limited to, 5-methylcytosine, 5-hydroxymethylcytosine, 5-formylcytosine and 5-carboxylcytosine. The one or more molecule separation and sequencing processes 506 can separate nucleic acid molecules extracted from plurality of samples 504 into a number of partitions with individual partitions corresponding to different levels of methylation. For example, the molecule separation and processes 506 can produce a first partition of nucleic acid molecules having first levels of methylation, a second partition of nucleic acid molecules having second levels of methylation, and a third partition of nucleic acid molecules having third levels of methylation. In various examples, the second levels of methylation can be greater than the first levels of methylation and the third levels of methylation can be greater than the first levels of methylation and the second levels of methylation. In one or more illustrative examples, the molecule separation proceeds of the one or moremolecule separation and sequencing processes 506 can include the first molecule separation process 122 and the second molecule separation process 136 described with respect to Figure 1.

[0278] The sequencing processes included in the molecule separation and sequencing processes 506 can be performed by one or more sequencing machines that produce negative sample sequencing data 508. In one or more examples, the negative sample sequencing data 508 can include sequencing reads that correspond to nucleic acid molecules derived from the plurality of samples 504 having at least threshold levels of methylation. In one or more illustrative examples, negative sample sequencing data 508 can include sequencing reads corresponding to nucleic acid molecules having at least a threshold amount of methylation in CG regions of the nucleic acid molecules. In one or more additional illustrative examples, the negative sample sequencing data 508 can include sequencing reads corresponding to nucleic acid molecules that are hypermethylated.

[0279] The framework 500 can also include a computing system 510. The computing system 510 can obtain the negative sample sequencing data 508 and then analyze the negative sample sequencing data 508 in conjunction with data corresponding to the second training samples 422 and the third training samples 424 described with respect to Figure 4 to be used in training a classification model that can determine metrics indicating the presence of cancer or not in a subject The computing system 510 can include one or more computing devices that can include at least one of one or more desktop computing devices, one or more mobile computing devices, or one or more server computing device. In various examples, at least a portion of the one or more computing devices implementing the computing system 510 can be included in a remote computing environment, such as a cloud computing environment. In one or more examples, the computing system 510 and the equipment used to perform the molecule separation and sequencing processes 506 can be implemented owned, operated, maintained, and / or controlled by a single organization. In one or more additional examples, the computing system 510 and the molecule separation and the equipment used to perform the sequencing processes 506 can be implemented, owned, operated, maintained, and / or controlled by multiple organizations. In one or more illustrativeexamples, the sequencing operations included in the molecule separation and sequencing processes 506 can include the operations performed by the sequencing machine 140 described with respect to Figure 1 and the sequencing machine 202 described with respect to Figure 2.

[0280] The computing system 510 can include a training data analysis system 512. In one or more examples, the training data analysis system 512 can perform at least a portion of the operations described with respect to the training data analysis system 412 of Figure 4. The training data analysis system 512 can determine values of quantitative measures of samples that are used in the training of the second computational model. For example, the training data analysis system 512 can determine pseudovalues for negative training samples 514. In one or more examples, the training data analysis system 512 can determine one or more predetermined values for individual samples of the plurality of samples 506 that correspond to the plurality of subjects 502 in which a tumor is not detected. In various examples, the pseudovalues for negative training samples 514 can correspond to values for mutant allele fractions of the plurality of samples 502. In one or more illustrative examples, at least a portion of the pseudovalues for the negative training samples 504 can have negative values. In one or more additional illustrative examples, at least a portion of the pseudovalues for the negative training samples 504 can have a same value. In one or more further examples, at least a portion of the pseudovalues for the negative training samples 504 can have a different value. In one or more scenarios, the pseudovalues for negative training samples 514 can be determined through one or more experimental processes to determine optimal values for the pseudovalues for negative training samples 514 to produce the second computational model, such that the second computational provides accurate and reliable output indicating the presence or absence of cancer in subjects.

[0281] The training data analysis system 512 can also determine quantitative measures for second training samples 516. The quantitative measures for second training samples 516 can correspond to the sample quantitative measures 414 generated by the first computational model 412 and that correspond to the second training samples 422 as described with respect to Figure 4. To illustrate, the quantitative measures for second training samples 516 can include a portion of the sample quantitative measures 414 thatcorrespond to nucleic acid molecules of a subset of the samples of the plurality of samples 404 for which one or more somatic mutations are present.

[0282] The training data analysis system 512 can also determine first sample weights 518 for the pseudovalues for negative training samples 514 and second sample weights 520 for the quantitative measures for second training samples 516. The first sample weights 518 and the second sample weights 520 can indicate weightings of the pseudovalues for negative training samples 514 and the quantitative measures for second training samples 516 during a training process for the second computational model. In one or more examples, at least a portion of the first sample weights 518 can be different from the second sample weights 520. In one or more additional examples, at least a portion of the first sample weights 518 can be the same as the second sample weights 520.

[0283] The computing system 510 can perform a second computational model training process 522. The second computational model training process 522 can include a number of iterations. In one or more examples, the training data used during different iterations of the second computational model training process 522 can be different. For example, first training data used during one or more first iterations of the second computational model training process 522 can be different from second training data used during one or more second iterations of the second computational model training process 522. In one or more additional examples, at least a portion of the training data used during the second computational model training process 522 can be common for each iteration of the second computational model training process 522. In still other examples, values for at least a portion of the training data used during the second computational model training process 522 can be the same during each iteration of the second computational model training process 522. In one or more illustrative examples, each iteration of the second computational model training process 522 can use the pseudovalues for negative training samples 514 and the quantitative measures for second training samples 516.

[0284] In the illustrative example of Figure 5, the second computational model training process can include a first training process iteration 524. The first training process iteration 524 can produce an initial version of the second computational model 528. The first training process iteration 524 can use the pseudovalues for negative training samples514, the first sample weights 518, the quantitative measures for second training samples 516, and the second sample weights 520. Additionally, the first training process iteration 524 can use third training sample sequencing data 528. The third training sample sequencing data 528 can include sequence representations of nucleic acid molecules derived from one or more samples of the plurality of samples 404 described with respect to Figure 4 that correspond to subjects in which a tumor is detected, that have sample quantitative measures 414 within a specified range corresponding to the first analysis criteria 418, and that have nucleic acid sequences for which somatic variants are not present in accordance with the second analysis criteria 420.

[0285] In one or more illustrative examples, the first training process iteration 524 can use the pseudovalues for negative training samples 514, the first sample weights 518, the quantitative measures for second training samples 516, and the second sample weights 520 to generate the initial version of the second computational model 526. The first training process iteration 524 can then apply the initial version of the second computational model 526 to the third training sample sequencing data 528 to produce quantitative measures for third training samples 532. In at least some examples, the quantitative measures for third training samples 530 can correspond to values related to mutant allele fractions for the third training samples 424. The quantitative measures for third training samples 530 can then be used in conjunction with the pseudovalues for negative trainings samples 514, the quantitative measures for second training samples 516, the first sample weights 518, and the second sample weights 520 in subsequent iterations of the second computational model training process 524. Although not shown in the illustrative example of Figure 5, the quantitative measures for third training samples 530 can be associated with additional sample weights that can be applied to values of the quantitative measures for third training samples 530.

[0286] In at least some examples, at least a portion of the quantitative measures for the third training samples 530 can be determined using a specified value that is based on a statistical analysis of the quantitative measures for the third training samples 530. For example, the computing system 510 can determine a plurality of groups of values for the quantitative measures for the third training samples 530. To illustrate, the computing system 510 can determine a number of quantiles for the quantitative measures for thethird training samples 530. The individual quantiles can be associated with a given range of values of the quantitative measures for the third training samples 530. In at least some examples, the computing system 510 can determine a default quantitative measure value for one or more third samples in one or more of the quantiles. In various examples, the default value can correspond to a cutoff value for another quantile determined by the computing system 510. In various examples, for a portion of the third samples having quantitative measures below a 50% quantile, below a 60% quantile, below a 70% quantile, below a 75% quantile, below an 80% quantile, below an 85% quantile, below a 90% quantile, below a 95% quantile, or below a 99% quantile, the computing system 510 can determine that the quantitative measure values for the portion of the third samples are set to a cutoff value for the given quantile. In one or more illustrative examples, for a portion of the third samples having quantitative measure values below a 95% quantile, the computing system 510 can determine that the quantitative measure values for the portion of the third samples are set to a cutoff value for the 95% quantile. In one or more additional illustrative examples, for a portion of the third samples having quantitative measure values below a 90% quantile, the computing system 510 can determine that the quantitative measure values for the portion of the third samples are set to a cutoff value for the 90% quantile. In one or more further illustrative examples, for a portion of the third samples having quantitative measure values below an 85% quantile, the computing system 510 can determine that the quantitative measure values for the portion of the third samples are set to a cutoff value for the 85% quantile. In still other illustrative examples, for a portion of the third samples having quantitative measure values below a 80% quantile, the computing system 510 can determine that the quantitative measure values for the portion of the third samples are set to a cutoff value for the 80% quantile.

[0287] The second computational model training process 522 can include additional training process iterations 532. Individual iterations of the additional training process iterations 532 can generate Nth versions of the second computational model 534. For example, a second iteration included in the additional training process iterations 532 can produce a second version of the second computational model included in the Nth version of the second computational model 534 and a third iteration included in the additional training process iterations 532 can produce a third version of the secondcomputational model included in the additional training process iterations 532. The pseudovalues for negative training samples 514, the quantitative measures for second training samples 516, the first sample weights 518, the second sample weights 520, and the quantitative measures for third training samples 530 can be used in individual additional training process iterations 532. In various examples, for individual additional training process iterations 532, the Nth versions of the second computational model 534 can produce values for the quantitative measures for the third training samples 530. In this way, at least a portion of the values for the quantitative measures for third training samples 530 used in individual additional training process iterations 532 can be different than the values of the quantitative measures for third training samples 530 due to changes in the second computational model between different subsequent versions of the second computational model.

[0288] Although not shown in the illustrative example of Figure 5, the additional training process iterations 532 can be performed using in silico training data. The in silico training data can be produced using information derived from at least a portion of the plurality of samples 504 obtained from the plurality of subjects 502 in which a tumor is not detected and using information derived from one or more samples obtained from one or more subjects in which a tumor is detected. For example, in silico training data can be produced by the computing system 510 using at least a portion of the negative sample sequencing data 508 and at least a portion of the positive sample sequencing data 408 that corresponds to at least a portion of the plurality of samples 404 having sample quantitative measures 414 described with respect to Figure 4 that do not correspond to the first analysis criteria 418. To illustrate, the in silico training data can be produced by combining information related to a portion of the plurality of samples 404 obtained from one or more subjects of the plurality of subjects 402 for which a tumor is detected and that have respective sample quantitative measures 414 outside of a specified range of values and information related to one or more of the plurality of samples 504 obtained from one or more subjects of the plurality of subjects 504 for which a tumor is not detected. In at least some examples, the in silico training data can include at least one of sequencing data or quantitative measures for one or more individual in silico training samples.

[0289] In one or more examples, the second computational model training process 522 can include evaluating values of a loss function of the second computational model after one or more iterations of the second computational model training process 522. In various examples, the second computational model training process 522 can be stopped in response to values of the loss function corresponding to convergence of the second computational model. In one or more additional examples, the second computational model training process 522 can be stopped after a specified number of iterations. In at least some examples, the second computational model training process 522 can be stopped before convergence of the loss function to minimize overfitting of the second computational model. In one or more illustrative examples, the second computational training process 522 can be stopped after at least 2 iterations, at least 3 iterations, at least 4 iterations, at least 5 iterations, at least 6 iterations, at least 7 iterations, at least 8 iterations, at least 9 iterations, at least 10 iterations, at least 15 iterations, at least 20 iterations, at least 25 iterations, at least 50 iterations, or at least 100 iterations.

[0290] The second computational model training process 522 can produce a trained version of the second computational model 536. The trained version of the second computational model 536 can include a classification model having a number of variables and weights that correspond to features of the training samples that can be indicative of a tumor being present in subjects. In one or more examples, the trained version of the second computational model 534 can include a classification model having a number of variables and weights that correspond to at least one of methylation information with respect to classification regions, sequencing information, or somatic variant information that can be indicative of a tumor being present in subjects. The trained version of the second computational model 536 can produce a model output 538. The model output 538 can include an indication that a tumor is present in a subject or an indication that a tumor is not present in a subject. Additionally, the model output 538 can include a probability of cancer being present in a subject. Further, the model output 538 can indicate tumor fraction for one or more samples obtained from a subject. The model output 538 can also correspond to a measure related to mutant allele fraction of a sample obtained from a subject. In still other examples, the model output 538 can indicate a stage of cancer for asubject. In various examples, the model output 538 can indicate the presence of one or more types of cancer in a subject.

[0291] In one or more illustrative examples, the trained version of the second computational model 536 can determine the model output 538 by analyzing methylation data and sequencing data derived from one or more samples obtained from a subject in relation to classification regions of a reference sequence to generate the model output 538. In at least some examples, the trained version of the second computational model 536 can produce the model output for a same subject at different points in time. For example, the trained version of the second computational model 536 can determine the model output 538 using data derived from one or more samples obtained from a subject prior to one or more medical interventions being performed. Additionally, the trained version of the second computational model 536 can determine the model output 538 using data derived from one or more additional samples obtained from the subject after the one or more medical interventions are performed. In one or more examples, the one or more medical interventions can include at least one of surgery, chemotherapy, radiation therapy, or another cancer treatment. In at least some illustrative examples, the trained version of the second computational model 536 can implement at least a portion of the processes, techniques, frameworks, and architectures described with respect to Figure 1 , Figure 2, and / or Figure 3 to generate the model output 538.

[0292] In various examples, the second computational model training process 522 can be performed for multiple instances of the second computational model. After the second computational model training process 522 is performed for each instance of the second computational model, the trained version of the second computational model 536 can be produced using a combination of features of the multiple instances of the second computational model. In one or more illustrative examples, the computing system 510 can implement the second computational model training process 522 using at least the pseudovalues for negative training samples 514, the quantitative measures for second training samples 516, the first sample weights 518, the second sample weights 520, the third training sample sequence data 528, the quantitative measures for third training samples 530, in silico training data, or one or more combinations thereof with respect to a first instance of the second computational model to generate a first trained version ofthe second computational model. The computing system 510 can also implement the second computational model training process using at least the pseudovalues for negative training samples 514, the quantitative measures for second training samples 516, the first sample weights 518, the second sample weights 520, the third training sample sequence data 528, the quantitative measures for third training samples 530, in silico training data, or one or more combinations thereof with respect to one or more second instances of the second computational model to generate one or more second trained versions of the second computational model. Features of the first trained version of the second computational model and the one or more second trained versions of the second computational model can then be combined to produce the trained version of the second computational model 536. In at least some examples, average values of variable weights of the first trained version of the second computational model and the one or more second trained versions of the second computational model, average values of parameters of the first trained version of the second computational model and the one or more second trained versions of the second computational model, and average values of other features of the first trained version of the second computational model and the one or more second trained versions of the second computational model can be generated to produce the trained version of the second computational model 536. In various examples, one or more combinations of variables included in the first trained version of the second computational model and the one or more second trained versions of the second computational model can be included in the trained version of the second computational model 536.

[0293] In one or more examples, multiple instances of the trained version of the second computational model 536 can be produced by the computing system 510 with individual instances of the trained version of the second computational model 536 corresponding to one or more specified cancer types. For example, the computing system 510 can produce at least two of a first trained version of the second computational model that corresponds to one or more first cancer types, a second trained version of the second computational model that corresponds to one or more second cancer types, a third trained version of the second computational model that corresponds to one or more third cancer types, a fourth trained version of the second computational model that corresponds toone or more fourth cancer types, a fifth trained version of the second computational model that corresponds to one or more fifth cancer types, a sixth trained version of the second computational model that corresponds to one or more sixth cancer types, a seventh trained version of the second computational model that corresponds to one or more seventh cancer types, an eighth trained version of the second computational model that corresponds to one or more eighth cancer types, a ninth trained version of the second computational model that corresponds to one or more ninth cancer types, or a tenth trained version of the second computational model that corresponds to one or more tenth cancer types, In various examples, the computing system 510 can generate trained versions of the second computational model 536 to detect up to 12 cancer types, up to 13 cancer types, up to 14 cancer types, up to 15 cancer types, up to 16 cancer types, up to 17 cancer types, up to 18 cancer types, up to 19 cancer types, up to 20 cancer types, or more.

[0294] To produce the different instances of the trained version of the second computational model 536 that correspond to an individual cancer type or a specified set of cancer types, the second computational model can be trained by the computing system 510 using training data that corresponds to the individual cancer type or the specified set of cancer types. For example, the computing system 510 can implement the training data analysis system 512 to generate quantitative measures for second training samples 516, where the second training samples are derived from individuals in which one or more somatic mutations corresponding to an individual cancer type or a specified set of cancer types are present. To illustrate, in scenarios where the computing system 510 is producing a trained version of the second computational model 536 that detects the presence of one or more colorectal cancers, the training data analysis system 512 can generate quantitative measures for second training samples 516 using data derived from subjects in which the one or more colorectal cancers are present. In one or more additional examples, in scenarios where the computing system 510 is producing a trained version of the second computational model 536 that detects the presence of one or more lung cancers, the training data analysis system 512 can generate quantitative measures for second training samples 516 using data derived from subjects in which the one or more lung cancers are present, in one or more further examples, in scenarios where thecomputing system 510 is producing a trained version of the second computational model 536 that detects the presence of one or more breast cancers, the training data analysis system 512 can generate quantitative measures for second training samples 516 using data derived from subjects in which the one or more breast cancers are present.

[0295] After the trained version of the second computational model 536 has been produced, the trained version of the second computational model 536 can be implemented with respect to one or more samples obtained from test subjects to generate the model output 538 for the individual test subjects. In implementations where the computing system 510 produces multiple trained versions of the second computational model to detect multiple cancer types, individual instances of the trained second computational model can provide model output. In one or more examples, the model output can indicate a probability of one or more cancer types being present in the test subject. For example, a first trained version of the second computational model can determine a first model output indicating one or more first probabilities of one or more first cancer types being present in test subjects, a second trained version of the second computational model can determine a second model output indicating one or more second probabilities of one or more second cancer types being present in test subjects, and a third trained version of the second computational model can determine a third model output indicating one or more third probabilities of one or more third cancer types being present in test subjects. In one or more illustrative examples, the computing system 510 can produce a first trained version of the second computational model that determines a first indication of colorectal cancer being present in a test subject, a second trained version of the second computational model that determines a second indication of lung cancer being present in a test subject, and a third trained version of the second computational model that determines a third indication of breast cancer being present in a test subject.

[0296] In various examples, the model outputs generated by multiple instances of the trained version of the second computational model can be analyzed to determine an overall output indicating at least one type of cancer present in a test subject. In one or more examples, individual instances of the trained version of the second computational model can produce a probability of a given type of cancer being present in a test subject.The computing system 510 can determine a model output having a highest probability and generate an indication that the cancer corresponding to the highest probability is present in the test subject. In some instances, the computing system 510 can determine a model output having a highest score and generate an indication that the cancer corresponding to the highest score is present in the test subject. In at least some examples, the computing system 510 can analyze output from multiple instances of the trained version of the computational model with respect to a threshold value. The threshold value can correspond to a minimum probability for determining that a given type of cancer is present in a test subject. In one or more additional examples, the threshold value can correspond to a minimum tumor fraction for determining that a given type of cancer is present in a test subject. In at least some examples, the computing system 510 can determine that the output from more than one trained version of the second computational model is at least a threshold value. In these scenarios, the computing system 510 can determine that more than one cancer type is present in a test subject. Further, in the scenarios where the computing system 510 determines that the output from more than one trained version of the second computational model is at least a threshold value, the computing system 510 can determine that cancer has metastasized in a test subject.

[0297] In one or more examples, the computing system 510 can implement one or more additional computational models to analyze the output from a number of instances of the trained second computational model. The one or more additional computational models implemented by the computing system 510 to analyze output from multiple instances of the trained version of the second computational model can include one or more machine learning models or one or more statistical models. In one or more illustrative examples, output from individual instances of the trained version of the second computational model can be assigned weights by the computing system 510 to determine a type of cancer present in a test subject.

[0298] Figure 6 is a diagrammatic framework 600 of a process to train a computational model using biological sample data and in silico training data, in accordance with one or more example implementations. The framework 600 can include a computing system 602. In one or more examples, the computing system 602 canperform at least a portion of the operations described with respect to at least one of the computing system 214 of Figure 2 and Figure 3, the computing system 410 of Figure 4, or the computing system 510 of Figure 5. Additionally, the computing system 602 can include a training data analysis system 604. In various examples, the training data analysis system 604 can perform at least a portion of the operations described with respect to the training data analysis system 416 of Figure 4 and the training data analysis system 512 of Figure 5.

[0299] Training sample methylation and sequencing data 606 can be accessed by the computing system 602. The training sample methylation and sequencing data 606 can include sequence representations of nucleic acid molecules derived from samples obtained from a plurality of subjects. The training sample methylation and sequencing data 606 can also include methylation data indicating methylation states of nucleotides of the nucleic acid molecules. In one or more illustrative examples, the training sample methylation and sequencing data 606 can indicate methylation states of cytosines of the nucleic acid molecules. In one or more additional illustrative examples, the training sample methylation and sequencing data 606 can indicate methylated cytosines of the nucleic acid molecules. In one or more further illustrative examples, the training sample methylation and sequencing data 606 can include sequencing representations and methylation state data of nucleic acid molecules having one or more CG regions with at least a threshold amount of methylation. For example, the training sample methylation and sequencing data 606 can include sequence representations that correspond to nucleic acid molecules that are identified as being included in a hypermethylated partition. A first portion of the training sample methylation and sequencing data 606 can include sequence representations and methylation states of nucleic acid molecules derived from first samples obtained from first subjects in which a tumor is detected. A second portion of the training sample methylation and sequencing data 606 can include sequence representations and methylation states of nucleic acid molecules derived from second samples obtained from second subjects in which a tumor is not detected.

[0300] In one or more examples, the training data analysis system 604 can analyze the training sample methylation and sequencing data 606 to determine residual positive training samples data 608 and negative training samples data 610. The training dataanalysis system 604 can also generate in-band positive training samples data 612. The residual positive training samples data 608 can include sequence representations and methylation data that correspond to nucleic acid molecules having a quantitative measure that is outside of a specified quantitative measure range and derived from samples obtained from subjects in which a tumor is detected. The negative training samples data 610 can include sequence representations and methylation data that correspond to nucleic acid molecules derived from samples obtained from subjects in which a tumor is not detected. In addition, the in-band positive training samples data 612 can include sequence representations and methylation data that correspond to nucleic acid molecules having a quantitative measure that is within the specified quantitative measure range and that are derived from samples obtained from subjects in which a tumor is detected. In one or more illustrative examples, the specified quantitative measure range can correspond to a range of mutant allele fraction values.

[0301] The computing system 602 can also include an in silico sample system 614 that generates in silico training samples 616. The in silico sample system 614 can analyze the residual positive training samples data 608 and the negative training samples data 610 to generate the in silico training samples 616. In one or more examples, the in silico sample system 614 can combine at least one of first quantitative measures or first sequence representations corresponding to first nucleic acid molecules represented in the residual positive training samples data 608 with at least one of second quantitative measures or second sequence representations corresponding to second nucleic acid molecules represented in the negative training samples data 610. In one or more illustrative examples, the in silico sample system 614 can combine a first portion of data from one or more first samples corresponding to the residual positive training samples date 608 with a second portion of data from one or more second samples corresponding to the negative training samples data 610 to produce one or more in silico training samples 616 having quantitative measures within the specified quantitative measure range. In various examples, the in silico sample system 614 can combine a first portion of data from one or more first samples corresponding to the residual positive training samples date 608 with a second portion of data from one or more second samples corresponding to the negative training samples data 610 to reduce one or more values ofthe quantitative measure for one or more samples corresponding to the residual positive training samples data 608 to produce in silico training samples 616 having modified quantitative measures values within the specified quantitative measure range.

[0302] In one or more additional illustrative examples, for a given in silico training sample 616, a proportion of one or more residual positive training samples that is combined with a proportion of one or more negative training samples can be 5 / 95, 10 / 90, 15 / 85, 20 / 80, 25 / 75, 30 / 70, 35 / 65, 40 / 60, 45 / 55, or 50 / 50. In various illustrative examples, an amount of one or more residual positive training samples that is combined with one or more negative training samples can be a numerical value that can be represented by a percentage value, a fraction, or a decimal value less than 1. In one or more further illustrative examples, the in silico training samples 616 can have sequence representations that correspond to the proportion of the one or more residual positive training samples that is combined with a proportion of one or more negative training samples. To illustrate, an individual in silico training sample 616 can be generated by combining a first residual positive sample and a first negative training sample. In situations where the proportion of amount of data of the first residual positive sample and the first negative training sample is 20 / 80, the in silico training sample 616 can have 20% of the sequence representation of the first positive training sample and 80% of the sequence representation of the first negative training sample. In still other examples, the in silico training sample 616 can have 5.275% of the sequence representation of the first positive training sample and 94.725% of the sequence representation of the first negative training sample. In one or more additional illustrative implementations, the in silico training sample 616 can have 4.725% of the sequence representation of a first positive training sample, 5.370% of the sequence representation of a second positive training sample, and 89.905% of a negative training sample In this way, the in silico training samples 616 can represent a hybrid of one or more residual positive training samples and one or more negative training samples.

[0303] The computing system 602 can include a quantitative measures model 618 that analyzes the in silico training samples 616 to generate in silico training samples data 620. In one or more examples, the quantitative measures model 618 can generate quantitative measures included in the in silico training samples data 620 that correspondto the in silico training samples 616. In this way, the in silico training samples data 620 can include at least one of a sequence representation or a quantitative measure that corresponds to individual in silico training samples 616. In one or more illustrative examples, the quantitative measures model 618 can generate mutant allele fraction values for the individual in silico training samples 616.

[0304] In various examples, the in silico training samples data 620 can be used in conjunction with the negative samples training data 610 and the in-band positive samples training data 612 to generate a classification computational model 622. For example, the in silico training samples data 620, the negative samples training data 610, and the in- band positive samples training data 612 can be used in a training process for the classification computational model 622. In at least some examples, the training process for the classification computational model 622 can the same as or similar to the training process of the second computational model described with respect to Figures 4 and 5. In one or more illustrative examples, the classification computational model 622 can produce an output that includes an indication of cancer for a given subject. In at least some examples, the indication of cancer for a given subject can include in indication that cancer is present in a subject or an indication that cancer is absent in a subject. The indication of cancer for the given subject can also include at least one of a probability of cancer being present in the given subject or a tumor fraction for the given subject. In one or more additional examples, the indication of cancer for a given subject can correspond to a stage of cancer present in a subject and / or one or more types of cancer.

[0305] In this way, the framework 600 can implement at least three models to generate the classification computational model 622. For example, a first model can be implemented to determine quantitative measures for at least a portion of the samples obtained from subjects in which cancer is present. The training data analysis system 604 can use the quantitative measures generated by the first model to determine the residual positive trainings samples data 608 and the in-band positive training samples data 612. In one or more illustrative examples, the first model can correspond to the first computational model 412 described with respect to Figure 4. The second model can correspond to the quantitative measures model 618. The quantitative measures model 618 can include a quantitative measures generator that determines quantitative measuresfor individual samples. The quantitative measures model 618 can be trained on data that is at least partially different from the data used to train the first model. In various examples, the quantitative measures model 618 is not a classification model and does not generate an indication of cancer for a given subject. Further, the third model can comprise the classification computational model 622. In these scenarios, the classification computational model 622 determine an indication of cancer for one or more subjects based on the information generated by the first model and the second model.

[0306] Figure 7 is a flowchart of an example method 700 to determine tumor metrics in a subject based on levels of methylation of classification regions, according to one or more implementations. At operation 702, the method 700 can include obtaining training sequence data including training sequencing reads derived from a plurality of samples of a plurality of subjects. Individual training sequencing reads can include a nucleotide sequence corresponding to a fragment of a nucleic acid included in a sample of the plurality of samples. Individual training sequencing reads can have a threshold amount of molecules with a methylated cytosine included in regions of the nucleotide sequence having at least a threshold cytosine-guanine content. In one or more illustrative examples, the plurality of samples can include cell-free nucleic acids. In one or more examples, methylated cytosines can be determined using at least one of (i) sodium bisulfite conversion and sequencing, (ii) Tet-assisted bisulfite sequencing (TAB-Seq), differential enzymatic cleavage, (iii)MBD partitioning, and / or treatment with MSRE and / or MDRE, or (iv) other conversion procedures using enzymes - e.g., Enzymatic Methyl Sequencing (EM-Seq),...

Claims

CLAIMSWHAT IS CLAIMED IS:1 . A method comprising: obtaining training sequence data including training sequencing reads derived from a plurality of samples of a first plurality of subjects, wherein a tumor is detected in the first plurality of subjects; determining, using a first computational model and based on the first training sequence data, individual values of a quantitative measure for individual samples of the plurality of samples, the individual values of the quantitative measure indicating an amount of mutant alleles present in first nucleic acids of the individual samples; analyzing the individual values of the quantitative measure to determine a subset of the plurality of samples having respective values of the quantitative measure within a specified range of values; determining a first group of training samples from the subset of the plurality of samples having nucleic acids with one or more somatic mutations present; obtaining a second group of training samples derived from a second plurality of subjects, wherein a tumor is not detected with respect to the second plurality of subjects; performing a training process for a second computational model using training data derived from the first group of training samples and the second group of training samples to produce a trained version of the second computational model; analyzing, using the second computational model, test sequencing reads derived from one or more samples of one or more test subjects to determine an indication of cancer being present in the one or more test subjects.

2. The method of claim 1 , wherein the training process for the second computational model includes a first iteration that comprises: determining first training data corresponding to the first group of training samples and including the respective values of the quantitative measure within the specified range of values; determining second training data including one or more pseudo values for the quantitative measure for the second group of training samples; anddetermining an initial version of the second computational model based on the first training data and the second training data.

3. The method of claim 2, comprising: analyzing the subset of the plurality of samples to determine a third group of training samples in which somatic mutations are absent; and determining, using the initial version of the second computational model and based on additional training sequences derived from the third group of training samples, additional individual values of the quantitative measure that correspond to individual training samples of the third group of training samples.

4. The method of claim 3, comprising: obtaining third training data that includes at least a portion of the additional individual values of the quantitative measure that correspond to the individual training samples of the third group of training samples; and wherein the training process for the second computational model includes a second iteration that comprises: determining a subsequent version of the second computational model based on the first training data, the second training data, and the third training data.

5. The method of claim 4, comprising: determining, based on further training sequences derived from the second group of training samples, further individual values of the quantitative measure; determining a threshold value for the quantitative measure that corresponds to at least a threshold number of the second group of training samples; determining that one or more third samples have respective additional individual values of the quantitative measure that are less than the threshold value; and modifying the respective additional individual values of the quantitative measure to correspond to the threshold value in the third training data.

6. The method of any one of claims 1-5, comprising:determining, for the training process of the second computational model, first weights for the plurality of samples of the first plurality of subjects, wherein the first weights are based on a first number of the plurality of samples; and determining, for the training process of the second computational model, second weights for the second group of training samples derived from the second plurality of subjects, wherein the second weights are based on a second number of the second group of training samples and an additional weighting factor.

7. The method of any one of claims 1-6, wherein the training process of the second computational model comprises a loss function.

8. The method of claim 7, wherein the loss function includes a Huber loss function, a support vector regression loss function, a ridge loss function, a lasso loss function, an elastic net loss function, or a square error loss function.

9. The method of claim 7, wherein the training process of the second computational model includes a plurality of iterations and individual iterations of the plurality of iterations are stopped before convergence of a Huber loss function.

10. The method of any one of claims 1 -9, wherein the second computational model comprises a linear regression model.

11. The method of any one of claims 1-10, wherein the second computational model is included in a plurality of computational models that determine indications of cancer being present in individuals, the method comprising: determining a plurality of groupings of the training data, wherein individual groupings of the plurality of groupings of the training data include a training portion and a validation portion; and performing training processes for the plurality of computational models using the plurality of groupings of the training data.

12. The method of claim 11 , wherein determining indications of cancer being present in one or more subjects includes performing one or more statistical operations based on output from each computational model of the plurality of computational models.

13. The method of any one of claims 1-12, comprising: analyzing the individual values of the quantitative measures to determine an additional subset of the plurality of samples having additional respective values of the quantitative measure outside of the specified range of values; identifying one or more first samples from among the additional subset of the plurality of samples; and identifying one or more second samples from among an additional plurality of samples, the additional plurality of samples being obtained from subjects in which a tumor is not detected.

14. The method of claim 13, comprising: combining a first portion of the training sequence data that corresponds to the one or more first samples with a second portion of the training sequence data that corresponds to the one or more second samples to determine additional training sequence data for an additional training sample, wherein an additional sequence representation of the additional training sample includes an amount of first nucleotides corresponding to the one or more first samples and an amount of second nucleotides corresponding to the one or more second samples; and determining, by a third computational model and based on the additional sequence representation, an additional quantitative measure for the additional training sample, wherein a value of the additional quantitative measure is less than first values of the quantitative measure for the one or more first samples and greater than second values of the quantitative measure for the one or more second samples.

15. The method of any one of claims 1-14, wherein: a plurality of types of cancer are detected in the first plurality of subjects; andthe second computational model determines a plurality of indications of cancer being present in the one or more test subjects, individual indications of cancer being present in the one or more test subjects corresponding to an individual type of cancer of the plurality of types of cancer.

16. The method of any one of claims 1-15, wherein a single type of cancer is detected in the first plurality of subjects and the indication of cancer being present in the one or more test subjects corresponds to the single type of cancer.

17. The method of any one of claims 1-16, wherein the indication of cancer being present in the one or more test subjects includes a first result indicating a tumor being detected or a second result indicating a tumor not being detected with respect to individual test subjects of the one or more test subjects.

18. The method of any one of claims 1-17, wherein the indication of cancer being present in the one or more test subjects includes a numerical value on a scale with the numerical value corresponding to at least one of a stage of cancer present in individual test subjects of the one or more test subjects, a probability of cancer being present in individual test subjects of the one or more test subjects, an estimate of tumor fraction for the individual test subjects of the one or more test subjects, or a progression of cancer present in individual test subjects of the one or more test subjects.

19. The method of any one of claims 1-18, wherein individual training sequencing reads include a nucleotide sequence corresponding to a fragment of a nucleic acid included in a sample of the plurality of samples, and the method comprises: analyzing the training sequencing reads to determine a first region quantitative measure derived from the training sequencing reads that corresponds to individual classification regions of a plurality of classification regions, at least a portion of the individual classification regions of the plurality of classification regions corresponding to genomic regions of a reference genome that have the threshold amount of methylatedcytosines in subjects in which cancer is detected and that have at least the threshold cytosine-guanine content; analyzing the training sequencing reads to determine a second region quantitative measure derived from the training sequencing reads that correspond to a plurality of control regions, individual control regions of the plurality of control regions corresponding to additional genomic regions of the reference genome that have at least the threshold cytosine-guanine content and that have at least the threshold amount of methylated cytosines in subjects in which cancer is detected and in additional subjects in which cancer is not detected; and determining a metric for the individual classification regions of the plurality of classification regions based on the first region quantitative measure for the individual classification regions and the second region quantitative measure for the plurality of control regions.

20. The method of claim 19, wherein the individual values of the quantitative measure for individual samples of the plurality of samples are determined based on the metric for the individual classification regions.21 . The method of any one of claims 1-20, wherein individual training sequencing reads correspond to molecules have a threshold amount of methylated cytosines included in regions of the nucleotide sequence having at least a threshold cytosine-guanine content.

22. The method of any one of claims 1-21 , wherein the training process for the second computational model comprises; performing a plurality of training processes for a plurality of instances of the second computational model using the training data; determining, based on individual training processes of the plurality of training processes, at least one of weights of variables or values of parameters for individual instances of the second computational model; andcombining the at least one of weights of variable or values of parameter for the individual instances of the second computational model to determine an aggregate model that corresponds to the second computational model.

23. The method of any one of claims 1-22, wherein the indication of cancer being present in the one or more test subjects is a numerical value, and the method comprises: analyzing the indication of cancer being present in the one or more test subjects with respect to a threshold value; and determining that cancer is present in a test subject of the one or more test subjects in response to determining that the indication of cancer being present is at least the threshold value.

24. The method of claim 23, wherein the threshold value includes a tumor fraction or a probability of a type of cancer being present in the test subject.

25. The method of claim 23 or 24, wherein the threshold value corresponds to a minimum specificity of at least 90% with respect to the second computational model.

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