System and method for estimating tumor growth

Abstract

A method for estimating tumor growth dynamics includes acquiring, by one or more processors, progression-free survival (PFS) data for a plurality of patients, the PFS data indicating (i) a plurality of observation times and (ii) the number of patients among the plurality of patients who experienced a PFS event within a most recent time window at each of the plurality of observation times; determining, by the one or more processors, a population distribution of one or more patient-specific parameters based on the PFS data; acquiring, by the one or more processors, measured tumor growth data for a particular patient receiving drug treatment; estimating, by the one or more processors, tumor growth for the particular patient based on (i) the measured tumor growth data and (ii) the population distribution of the one or more patient-specific parameters; and causing, by the one or more processors, a visual representation of the estimated tumor growth for the particular patient to be presented on a display.

Description

[Technical Field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims the benefit of U.S. Provisional Patent Application No. 63 / 408,885, entitled "SYSTEMS AND METHODS FOR ESTIMATING TUMOR GROWTH," filed September 22, 2022, which is incorporated herein by reference in its entirety.

[0002] This application relates generally to tumor growth analysis in cancer patients, and more specifically to modeling and estimating contributions to tumor growth rate. [Background technology]

[0003] Tumor growth analysis is essential in experimental tumor research. Anti-cancer treatments work by reducing tumor growth over time by shrinking and / or slowing tumor growth, resulting in improved patient symptoms and increased overall survival. Progression-free survival (PFS) can be the length of time during and after treatment that a patient lives with the disease but does not worsen. PFS can predict overall survival. Summary of the Invention [Means for solving the problem]

[0004] In one aspect, a computer-implemented method for estimating tumor growth includes: obtaining, by one or more processors, progression-free survival (PFS) data for a plurality of patients, the PFS data indicating (i) a plurality of observation times and (ii) a number of patients among the plurality of patients at each of the plurality of observation times who experienced a PFS event within a most recent time window; determining, by the one or more processors, a population distribution of one or more patient-specific parameters based on the PFS data; obtaining, by the one or more processors, measured tumor growth data for a particular patient receiving drug treatment; estimating, by the one or more processors, tumor growth for the particular patient based on (i) the measured tumor growth data and (ii) the population distribution of the one or more patient-specific parameters; and causing, by the one or more processors, a visual representation of the estimated tumor growth for the particular patient to be presented on a display.

[0005] In some embodiments, determining a population distribution for the one or more patient-specific parameters includes determining a growth curve function that includes the one or more patient-specific parameters. In some embodiments, the growth curve function includes at least one of an exponential growth function, a logistic growth function, or an ordinary differential function. In some embodiments, the one or more patient-specific parameters include a baseline normalized sum of longest diameters (SLD) measurement parameter. In some embodiments, the one or more patient-specific parameters include a growth rate parameter.

[0006] In some embodiments, the growth rate parameter comprises a parameter for a baseline growth rate without treatment. In some embodiments, the one or more patient-specific parameters comprise a parameter related to the proportion of drug-sensitive tumor cells in a patient of the plurality of patients. In some embodiments, the value of the parameter related to the proportion of drug-sensitive tumor cells in a patient of the plurality of patients ranges from 0 to 1. In some embodiments, the growth curve function is time-dependent. In some embodiments, determining the population distribution of the one or more patient-specific parameters comprises fitting a growth curve function to observations at the plurality of observation time points.

[0007] In some embodiments, the growth curve function is a logistic growth function, and the one or more patient-specific parameters include multiple parameters of the logistic growth function. In some embodiments, estimating tumor growth for a particular patient includes modeling the tumor growth rate for the particular patient using a pharmacokinetic-pharmacodynamic (PKPD) model having a first term representing tumor size change in the particular patient not receiving drug treatment and a second term representing a contribution to tumor size change in the particular patient due to drug treatment, and jointly estimating one or more parameters of the first term and one or more parameters of the second term by fitting the PKPD model to measured tumor growth data, in part, by setting constraints on one or more parameters of the first term using population distributions of the one or more patient-specific parameters.

[0008] In some embodiments, the one or more parameters of the second term include one or more of: a drug concentration in the plasma of a particular patient; a maximum mortality rate of a particular patient; and a maximum median effective concentration (EC50). In some embodiments, estimating tumor growth further comprises obtaining an overall response rate for a particular patient receiving the drug treatment. In some embodiments, estimating tumor growth further comprises obtaining one or more non-target events for a particular patient receiving the drug treatment.

[0009] In some embodiments, the observations include, for each patient of the plurality of patients, a first observation at a first time indicating that the patient did not have a PFS event before the first time and a second observation at a second time indicating that the patient had a PFS event before the second time. In some embodiments, the PFS data corresponds to a particular cancer type, and estimating tumor growth for the particular patient includes estimating tumor growth for patients diagnosed with the particular cancer type. In some embodiments, causing the display to present a visual representation of the estimated tumor growth for the particular patient includes causing the display to display a trajectory of tumor growth for the particular patient if the particular patient had not received the drug treatment.

[0010] In some embodiments, the population distribution for one or more patient-specific parameters comprises a lognormal distribution. In some embodiments, the PFS data comprises at least one of a digitized PFS plot or a PFS risk table. In some embodiments, the PFS data indicates the number of patients among a plurality of patients who had a baseline normalized sum of longest diameter (SLD) measurement of at least 1.2 or developed new lesions at each of a plurality of observation times and within the most recent time window. In some embodiments, the plurality of patients represented by the PFS data are patients associated with ineffective drug treatment. In some embodiments, the method further comprises adjusting the dose of drug treatment based on the estimated tumor growth for a particular patient.

[0011] In another aspect, a computer system for estimating tumor growth is provided, the computing system including a data storage device storing processor-readable instructions and a processor configured to execute the instructions to perform a method, the method including: acquiring, by the one or more processors, progression-free survival (PFS) data for a plurality of patients, the PFS data indicating (i) a plurality of observation times and (ii) a number of patients, among the plurality of patients, at each of the plurality of observation times, who experienced a PFS event within a most recent time window; determining, by the one or more processors, a population distribution of one or more patient-specific parameters based on the PFS data; acquiring, by the one or more processors, measured tumor growth data for a particular patient receiving drug treatment; estimating, by the one or more processors, tumor growth for the particular patient based on (i) the measured tumor growth data and (ii) the population distribution of the one or more patient-specific parameters; and causing, by the one or more processors, a visual representation of the estimated tumor growth for the particular patient to be presented on a display.

[0012] In yet another aspect, a non-transitory computer-readable medium is provided that includes instructions for estimating tumor growth, the instructions, when executed by a processor, causing the processor to perform a method, the method including: acquiring, by one or more processors, progression-free survival (PFS) data for a plurality of patients, the PFS data indicating (i) a plurality of observation times and (ii) a number of patients, among the plurality of patients, at each of the plurality of observation times, that experienced a PFS event within a most recent time window; determining, by the one or more processors, a population distribution of one or more patient-specific parameters based on the PFS data; acquiring, by the one or more processors, measured tumor growth data for a particular patient receiving drug treatment; estimating, by the one or more processors, tumor growth for the particular patient based on (i) the measured tumor growth data and (ii) the population distribution of the one or more patient-specific parameters; and causing, by the one or more processors, a visual representation of the estimated tumor growth for the particular patient on a display.

[0013] Those skilled in the art will understand that the figures described herein are included for illustrative purposes and are not intended to limit the present disclosure. The figures are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the present disclosure. It should be understood that in some instances, various aspects of the described embodiments may be shown exaggerated or enlarged to facilitate understanding of the described embodiments. In the drawings, like reference characters generally refer to functionally similar and / or structurally similar components throughout the various views. [Brief explanation of the drawings]

[0014] [Figure 1] FIG. 1 is a simplified block diagram of an example of a system capable of implementing the tumor growth modeling and prediction techniques disclosed herein. [Figure 2] 1 shows an example of a progression-free survival (PFS) plot with associated risk table according to some embodiments of the technology described herein. [Figure 3] 1 is a plot showing an example of the selection of a single fixed PFS event time and associated exponential growth curve for a particular patient within a particular PFS window, according to some embodiments of the technology described herein. [Figure 4] 1 is a plot showing three exemplary possible PFS event times and associated exponential growth curves for a particular patient within a particular PFS window, according to some embodiments of the technology described herein. [Figure 5] 10 is a plot showing noise in SLD measurements over time for an example patient, in accordance with some embodiments of the technology described herein. [Figure 6] 1 shows tumor doubling times measured across a population of patients for each of a variety of cancer types, according to some embodiments of the technology described herein. [Figure 7]Figure 1 shows estimated drug concentrations in plasma (top row) and estimated tumor growth (bottom row) for three example combinations of drug dose and cancer type, according to some embodiments of the technology described herein, where estimated tumor growth shows tumor growth both with and without the drug. [Figure 8] FIG. 1 is a flow diagram of an example method for estimating tumor growth, according to some embodiments of the technology described herein. [Figure 9] 1 illustrates an exemplary process for generating data according to some embodiments of the techniques described herein. [Figure 10] 1 shows one or more exemplary post-hoc draws of SLD for a single patient from the control group who progressed on the second post-baseline scan, with ground truth values ​​overlaid in white, according to some embodiments of the techniques described herein. [Figure 11] 10 shows exemplary marginal posterior values ​​for each patient estimated from the model along with ground truth values, according to some embodiments of the techniques described herein. [Figure 12] 1 shows an exemplary post-hoc view of a test and group-specific parameters with their ground truth values ​​overlaid, according to some embodiments of the techniques described herein. [Figure 13] 1 shows exemplary plots relating PFS curves and total number of responses in each figure overlaid with observed values ​​in a post hoc predictive check (PPC) to assess the adequacy of the fit, according to some embodiments of the technology described herein. [Figure 14] 1 shows simulated response numbers and PFS curves for four arms of a simulated trial according to some embodiments of the technology described herein. [Figure 15] FIG. 1 is a schematic diagram of an exemplary computing device capable of implementing aspects described herein. DETAILED DESCRIPTION OF THE INVENTION

[0015] To evaluate the effectiveness of a drug in cancer patients (e.g., during early-phase drug trials), observations of tumor / lesion size can be collected over the period the drug is administered. While tumor growth rate measurements are useful, they can be insufficient because tumor growth rate can depend on two competing factors: one factor may be the rate at which the tumor would grow in the absence of drug treatment, and the other factor may be the rate at which the administered drug is shrinking the tumor. Without the ability to accurately estimate the individual contributions of each of these factors, it can be difficult to assess whether a drug is effective at all, let alone determine the best dosing regimen or which patient populations will benefit most from the drug.

[0016] A technique for isolating and assessing tumor growth rate in the absence of drug treatment (referred to herein as the "Kay technique") has been proposed, which uses data from progression-free survival (PFS) plots to estimate tumor size doubling time per "sum of longest diameters" (SLD) of a target lesion metric. See Kay et al., The AAPS Journal, 21:27, "Estimation of Solid Tumor Doubling Times from Progression-Free Survival Plots Using a Novel Statistical Approach" (2019). However, the Kay technique does not accurately account for certain uncertainties in PFS plots, such as uncertainty regarding where PFS events occurred in a given time window and uncertainty due to SLD measurement error / noise. Furthermore, the Kay technique strictly applies certain assumptions (e.g., exponential tumor growth).

[0017] Although some techniques and modeling methods can describe sum longest diameter (SLD) measurements and their sequential response over time to any administered drug treatment, data is usually not publicly available for these techniques and modeling methods. Furthermore, while some approaches can extract certain publicly available data and assume exponential growth due to their model assumptions, the extracted publicly available data may not be informative of the underlying tumor dynamics. Therefore, there remains a need for tumor growth modeling that can be more accurate and more flexible.

[0018] To address the aforementioned issues with tumor growth modeling, the systems and methods disclosed herein can provide a more flexible modeling approach for more accurately learning one or more parameters (e.g., patient-specific parameters related to tumor growth). The systems and methods disclosed herein can describe longitudinal sum longest diameter (SLD) measurements and their continuous response over time to any drug treatment administered in a specific longitudinal regimen. This can provide several advantages over traditional methods that typically consider snapshots in time. First, the systems and methods disclosed herein can capture the effect on response that may occur when exposures change over time, such as when a patient has dose reductions, different regimens, or exposures that reduce anti-drug antibodies. Second, because the entire longitudinal history of SLD is modeled, multiple quantities of interest, such as maximum regression, time to progression, time to maximum regression, or doubling time, can be captured in one unified model. The systems and methods disclosed herein can incorporate non-target progression events as time-to-event data modeled by a hazard function, which can go a step further and capture common endpoints such as progression-free survival (PFS) and overall response rate (ORR). Third, due to their semi-mechanistic nature, one or more parameters can have a mechanistic interpretation, enabling a rich set of simulation possibilities and facilitating generalization to new regimes. For example, estimates of certain parameters, such as rate constants (e.g., kill rates), can be borrowed or extrapolated from preclinical data or published studies to compare treatments under similar conditions or to estimate the efficacy of novel treatments.

[0019] The systems and methods disclosed herein can also address: how early Phase 1 results can be generalized to earlier lines of therapy by using one or more parameters (e.g., patient-specific or non-patient-specific parameters) to capture the dynamics of groups of patients on different lines of therapy; how a drug can perform in a one-to-one match with existing standard of care by using one or more parameters to capture drug-specific effects; how a drug can perform in combination with existing standard of care by combining one or more parameters to simulate the combination; and how many patients can be recruited in a clinical trial to demonstrate these results in a statistically significant way by simulating the entire clinical trial using the systems and methods disclosed herein to account for changes at all levels.

[0020] Although individual SLD data are not typically published, endpoints such as PFS and ORR derived directly from the individual data are often published. Because the relationship between such published data and the underlying individual SLD data is inherently causal and unidirectional, publicly available endpoints such as PFS and ORR can be used to infer parameters in the systems and methods disclosed herein, following a specific set of rules. In some circumstances, certain parameters can be estimated from individual SLD data from external datasets. One or more parameters capturing the dynamics of a cohort with an earlier line of treatment can be learned from data from a cohort not available in Phase 1. The tumor kill rate of another drug can be learned from data on patients receiving that drug.

[0021] The systems and methods disclosed herein can provide a highly flexible and general framework for modeling how a set of observed data can arise from a set of underlying causes using Bayesian generative models, or probabilistic graphical models. Such models can be represented by probability diagrams that encode the joint probability distribution between unobserved variables and observed data and can be commonly used in Bayesian statistics and machine learning methods. This joint distribution can then be used to infer causal relationships and parameters of interest by conditioning the observed data and applying Bayes' rule. This Bayesian inversion inference process has become particularly easy and flexible in recent years with the emergence of several probabilistic programming languages, such as BUGS, JAGS, Stan, PyMC3, Turing, and Pyro. Advantages of using Bayesian generative models include specifying that the data generation process (conditional distribution) is natural and can provide a joint distribution; because Bayesian inference can include joint distributions, specifying the model in a probabilistic programming language (PPL) by simply coding the generation process; and implementing arbitrarily complex distributions, numerical methods, or constraints.

[0022] Using Bayesian generative models, the systems and methods disclosed herein can estimate general tumor dynamics information from published studies containing PFS and ORR information. Uncertainty in PFS data can be better accounted for by directly modeling tumor growth from PFS plots and / or risk table information, rather than randomly selecting a fixed event time for each patient (as in, for example, the Kay technique). In particular, the systems and methods disclosed herein can use a start and end time window as censored observations for that particular patient that have not yet experienced or have experienced an event with a baseline-normalized SLD reaching 1.2. By not artificially constraining each patient's event time to a specific fixed time, the overall distribution of the patient population reflected by the PFS data can more accurately reflect uncertainty, including uncertainty in PFS event times within a given window and uncertainty due to SLD measurement error or noise. Furthermore, the systems and methods disclosed herein may not assume a specific type of growth (e.g., exponential growth). The systems and methods disclosed herein can also be used to jointly estimate tumor growth parameters in conjunction with pharmacokinetic-pharmacodynamic (PKPD) parameters in a PKPD model. This may include parameters that indicate the contribution of both baseline (untreated) tumor growth and drug-related tumor shrinkage to overall tumor growth rate, which is difficult to estimate without supplemental and / or internal PFS data. The systems and methods disclosed herein may also be used to complement existing unpublished studies.

[0023] The systems and methods disclosed herein can provide a deeper and more accurate understanding of the contribution of tumor growth in patients across a variety of indications (e.g., biliary cancer, pancreatic cancer, testicular cancer, etc.). Furthermore, the systems and methods disclosed herein can enable modeling of drug effects without running a control group that does not receive drug treatment. This can then significantly reduce the amount of time, money, and / or other resources that may be spent before making important decisions, such as whether to proceed with a drug trial (e.g., whether to expand the drug trial to a larger patient population).

[0024] The various concepts described introductoryly above and discussed in more detail below can be implemented in any of many ways, and the concepts described are not limited to any particular embodiment format. Example implementations are provided for illustrative purposes.

[0025] FIG. 1 is a simplified block diagram of an example system 100 in which the systems and methods (e.g., tumor growth modeling and prediction techniques) disclosed herein may be implemented. System 100 includes a computing system 110 coupled to a patient database 112. Computing system 110 may be a single computing device or may include multiple co-located and / or distributed computing devices communicatively coupled by one or more networks. In the example embodiment shown in FIG. 1 , computing system 110 includes a processing unit 120, a network interface 122, a display 124, a user input device 126, and a memory 128. Processing unit 120 includes one or more processors, each of which may be a programmable microprocessor that executes software instructions stored in memory 128 to perform some or all of the functions of computing system 110 described herein. Alternatively, one, some, or all of the processors in processing unit 120 may be other types of processors (e.g., application specific integrated circuits (ASICs), field programmable gate arrays (FPGAs), etc.), and the functionality of computing system 110 described herein may instead be implemented partially or entirely in hardware. Memory 128 may include one or more physical memory devices or units, including volatile and / or non-volatile memory. Any suitable type or types of memory may be used, such as read-only memory (ROM), solid-state drives (SSDs), hard disk drives (HDDs), etc.

[0026] Network interface 122 may include any suitable hardware (e.g., front-end transmitter and receiver hardware), firmware, and / or software configured to communicate with external devices and / or systems (e.g., client devices, or one or more servers maintaining patient database 112) over one or more networks using one or more communication protocols. For example, network interface 122 may be or include an Ethernet interface, and / or may include a wireless local area network (LAN) interface, etc.

[0027] Display 124 may use any suitable display technology (e.g., LED, OLED, LCD, etc.) to present information to a user, and user input device 126 may be a keyboard or other suitable input device. In some embodiments, display 124 and user input device 126 are integrated into a single device (e.g., a touchscreen display). Generally, display 124 and user input device 126 may be combined to allow a user to interact with a user interface (e.g., a graphical user interface (GUI)) provided by computing system 110, such as that described in more detail below. However, in some embodiments, computing system 110 does not include display 124 and / or user input device 126, or one or both of display 124 and user input device 126 are included in another computer or system (e.g., a client device not shown in FIG. 1 ) communicatively coupled to computing system 110.

[0028] The memory 128 stores instructions for one or more software applications, including a tumor growth estimation application 130 (also referred to herein as "TGE application 130"). When executed by the processing unit 120, the TGE application 130 is generally configured to identify / learn distributions of one or more parameters (e.g., tumor growth model parameters) based on progression-free survival (PFS) data stored in the patient database 112, and to use the identified distributions to determine / learn (jointly estimate) parameters of a pharmacokinetic / pharmacodynamic (PKPD) model for each of one or more specific patients. The TGE application 130 can display estimated tumor growth or any information related to estimated tumor growth. The TGE application 130 includes a user interface unit 140, a data extraction unit 142, a population modeling unit 144, and a patient modeling unit 146. In general, the user interface unit 140 manages interaction with a user (e.g., a user operating the user input device 126 and the display 124), the data extraction unit 142 manages the retrieval of PFS data from the patient database 112 (and / or any pre-processing of the PFS data), the population modeling unit 144 learns the distribution of baseline (i.e., drug-free or ineffective) tumor growth across the population of patients represented by the PFS data, and the patient modeling unit 146 uses the learned population distribution and a particular patient's tumor size observations over time to model the contribution of both baseline tumor growth and drug treatment to the overall growth rate of the patient's tumor. The operation of the TGE application 130 and its various units 140-146 are described in further detail below.

[0029] The patient database 112 may include one or more databases, which may be stored in one or more memories at one or more co-located or remote locations. In some embodiments, the patient database 112 is local to the computing system 110 (e.g., stored in memory 128). The patient database 112 includes any information about multiple patients, such as PFS data for multiple patients, for each of one or more cancer indications / types. For example, the patient database 112 may include a digitized PFS plot and / or PFS risk table (e.g., of the type depicted in FIG. 2 ), or may include multiple PFS plots and / or PFS risk tables, each corresponding to a different cancer type (e.g., pancreatic, biliary, breast, etc.). In another example, the patient database 112 may include ORR.

[0030] The data extraction unit 142 is generally responsible for searching / retrieving desired PFS data from the patient database 112. In some embodiments, the data extraction unit 142 retrieves PFS data for a particular type of cancer based on user input detected by the user interface unit 140. For example, the user interface unit 140 may generate and / or input a GUI and cause the display 124 to present the GUI to the user. The user can then operate the user input device 126 to input an indication of the cancer type of interest via the GUI, and the data extraction unit 142 can retrieve PFS data (e.g., plots and / or risk tables) corresponding to the indicated cancer type. In some embodiments, the patient database 112 includes raw data (e.g., anonymized encounter data from a healthcare provider indicating dates and diagnoses / measurements / etc.), and the data extraction unit 142 constructs a PFS plot and / or a PFS risk table, or some other similar data structure. For example, the data extraction unit 142 may construct a digitized PFS plot from the raw data, or may generate the data in a more easily usable format (e.g., an indexed list of patient-specific entries, each indicating the start and end of a time window during which each patient had a PFS event).

[0031] The PFS data obtained by data extraction unit 142 may correspond to patients who have not received effective drug treatment (e.g., patients who were treated with an experimental drug that was later shown to be ineffective and / or patients who chose not to be treated with the drug). In this manner, population modeling unit 144 can use the PFS data to learn "baseline" growth rate patterns for tumors of a particular cancer type.

[0032] The population modeling unit 144 uses the obtained PFS data (optionally after formatting, cleaning, and / or other pre-processing of the PFS data by the data extraction unit 142) to identify a population distribution of one or more parameters (e.g., patient-specific parameters) of a growth curve function, i.e., to identify a distribution across the patient population represented by the obtained PFS data. To this end, the population modeling unit 144 first uses the PFS data to learn one or more parameters (e.g., one or more growth curve parameters) for each patient in the population. In some embodiments, the growth curve of a particular patient (patient i) as a function of time is generally referred to herein as f(t,θ i ), where θ i represents one or more growth curve parameters specific to that patient (also referred to herein as "patient-specific parameters" of the growth curve function). In some other embodiments, the growth curves of a particular patient (patient i) as a function of time can be referred to herein collectively as R(t), where t represents time. In some embodiments, the growth curve function R(t) is

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[0033] Some PFS plots may provide more detailed information (e.g., as seen in FIG. 2, where the trace shows the timing of PFS events at much finer granularity than the two-month window of the PFS risk table). In such cases, population modeling unit 144 may be able to leverage the more specific timing information to learn a more accurate distribution of growth curve parameters. However, in some cases, the more granular timing is the result of factors not fully captured in the modeling (e.g., the patient becoming sicker and being tested well before the next drug treatment), in which case population modeling unit 144 may instead ignore the more granular timing information of the PFS plot and use the PFS risk table information instead. This can introduce considerable uncertainty regarding the trajectory of a patient's growth curve. As seen in FIG. 4, for example, a particular patient's PFS event within the time window marked by start time 402 and end time 404 could have occurred at the time corresponding to PFS event 410, PFS event 412, or PFS event 414, or at any other time within the window. This uncertainty in each patient's estimates can affect the uncertainty in the estimates for the entire population. To avoid artificially removing that uncertainty (thereby losing useful information), population modeling unit 144 does not assume a fixed time for each patient's PFS event, but instead learns the distribution of growth curve parameters by directly using the start and end times of a time window in which a PFS event is known to have occurred (e.g., times 402 and 404 in FIG. 4 ) as censored observations. For example, from the PFS data (subject to measurement error), the patient's baseline normalized SLD is less than 1.2 at time point 402 and at least 1.2 at time point 404.

[0034] The population modeling unit 144 fits a particular type of distribution (e.g., a log-normal distribution) to the censored observations of the patients. In one embodiment, for example, the population modeling unit 144 fits a particular type of distribution (e.g., a log-normal distribution) to the censored observations of the patients.

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[0035] Using y(t) to represent the baseline normalized SLD, the population modeling unit 144 calculates: y(t)~LogNormal(f(t,θi),σ), P(y(t)<1.2 | f(t,θ),σ), P(y(t)>1.2 | f(t,θ),σ), θi~LogNormal(μ,ω) The population distribution of y(t) can be specified according to In the above equation, σ represents a noise parameter, and the ensemble modeling unit 144 calculates the parameter θ i The parameters μ and ω can be jointly estimated with the distribution of θ iare the mean and variance of the log-normal distribution learned for i (If x contains two or more parameters, it has multiple means and variances). Probabilities (P) are the probability / likelihood that a PFS event (baseline normalized SLD greater than 1.2) occurred or did not occur for a given patient at any time point t. Specifically, they are the integrals of the probability density functions of the log-normal distributions from 0 to 1.2 and from 1.2 to infinity, respectively.

[0036] In some embodiments, the growth curve of a particular patient (patient i) as a function of time can be referred to herein collectively as R(t), where t represents time. In some embodiments, the growth curve function R(t) is:

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[0037] To estimate the likelihood for a single subject, X itmay contain discrete SLD observations for the i-th patient at observation time t. The observations may be modeled as a log-normal distribution around the curve with some observation / model specification error noise σ:

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[0038] The progression criterion may be the first time that both of the following are true: 1. The observed SLD is 1.2 times the minimum observed SLD; 2. The observed SLD is at least 5 mm greater than the minimum observed SLD.

[0039] At each observation point, the progress criteria may include a threshold above which the observation is considered progress. Formally, this threshold is max{1.2min{X i0 ,···,X 0,t-1},min{X i0 ,···,X 0,t-1}+5}.

[0040] The patient arrives at time T i If a patient is considered to have progressed at , the likelihood of observing this patient given the patient-specific parameters is

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[0041] If a patient is right-censored after time Ti-1, the last term can be removed since the patient's progress status is unknown at that time.

[0042] The above likelihood may involve multidimensional integrals with no known closed-form solution. it can be sampled while enforcing the constraints of Stan. Thus, the likelihood is a probability density function (PDF of each observation:

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[0043] To generalize to population-level growth dynamics, the individual / patient-specific likelihood can be multiplied by the population distribution, and the product across all patients is

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[0044] Rather than marginalizing patient-specific parameters, patient-specific parameters can be sampled in Stan in addition to patient-specific and population observations.

[0045] ORR information from previous studies can be included in the likelihood. ORR, in other words, the number of patients who experience a response, can be given. The overall response rate can be the minimum observed value for a patient's tumor that is less than 0.7 times the baseline. The minimum observed value for any patient is MI:=min{X i1 ,···,X iT}, then ORR is

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[0046] In some embodiments, an approach with applicable soft constraints can be used to sample in Stan, and approximate Bayesian inference can be

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[0047] In some embodiments, progression may include situations such as when the SLD reaches a particular threshold. In some other embodiments, progression criteria may include beyond situations such as when the SLD reaches a particular threshold, but may also be due to non-target progression events such as the appearance of new lesions, progression of non-target lesions, symptomatic worsening, or death. To account for this, these non-target progression events may be modeled using a hazard function that is itself a function of tumor growth inhibition kinetics, using the following form:

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[0048] Hazard functions can include survival functions that can be incorporated into the likelihood of an individual patient:

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[0049] Otherwise, X iT If is greater than the SLD progression threshold, the patient may not have had non-target progression before time T, and that possibility is not excluded; therefore, the likelihood is reduced by the term

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[0050] In some embodiments, the GUI provided by user interface unit 140 allows the user to select or input a desired type of growth curve function and / or growth curve parameters (e.g., from a drop-down list of options), and population modeling unit 144 uses the selected function / parameters. In yet other embodiments, the GUI provided by user interface unit 140 allows the user to select a particular cancer type, after which data extraction unit 142 retrieves PFS data (from patient database 112) corresponding to a population of patients having that cancer type, and population modeling unit 144 automatically selects an appropriate a priori growth function for the selected cancer type.

[0051] Similar to the growth function, the population modeling unit 144 can assume any suitable type of distribution across the patient population represented by the PFS. i In the case of a lognormal distribution, the indication-specific parameter μ itself is given by the distribution μj ~LogNormal(α,τ) or distribution μ j ~LogNormal(α+βx i , τ), where x i are indication or study specific covariates, etc. In some embodiments, the GUI provided by the user interface unit 140 allows the user to select the parameters θ i The desired distribution type for can be selected or entered (e.g., from a drop-down list of options), and the population modeling unit 144 will use the selected distribution.

[0052] As mentioned above, modeling directly from censored observations (i.e., two censored observations per patient in a population) can offer several advantages. Direct modeling techniques allow for more accurate quantification of the uncertainty inherent in PFS plots and risk tables (discussed above), leading to more accurate predictions of when a PFS event is likely to occur. The system and method can also better account for other sources of uncertainty, such as SLD measurement / observation noise. Noisy SLD measurements can be very common and can result in, for example, a PFS event being detected in the wrong time window (e.g., if the PFS event actually occurs just before the beginning of the time window, but the tumor size measurement is slightly off). An example of SLD noise is shown in Figure 5, where each point represents a different observation / measurement.

[0053] Furthermore, direct modeling approaches are highly flexible, allowing for different growth curve functions and / or distribution types, as described above. For example, by directly modeling from PFS data in a probabilistic programming language, growth curves can take any form, as long as trajectories that plug into likelihoods / probabilities can be forward-solved. Different studies can also be modeled as having non-zero effects, as long as specific assumptions are made about specific PKPD characteristics. Population distributions for growth curves can be generalized in a probabilistic programming language as well. For example, more flexible distributions with more parameters or specific characteristics (e.g., biomodal, sparse, or heavier-tailed) can be used. Indication-level parameters can be derived from hierarchical distributions across indications (cancer types), allowing for information pooling (especially for less informative studies). The population modeling unit 144 can regress indication-level parameters to, for example, model progression rates as a function of prior lines of therapy. Several example population distributions for different cancer / disease indications / types are shown in Figure 6.

[0054] Yet another advantage is that the parameters (e.g., one or more parameters θ i and the noise parameter σ) can better inform the learning of these parameters.

[0055] After population modeling unit 144 identifies / learns the distribution of baseline tumor growth parameters across the population represented by the PFS data, patient modeling unit 146 uses that distribution and a particular patient's SLD observations / measurements over time to model the contributions of both baseline tumor growth and drug treatment to that patient's overall tumor growth rate. More specifically, patient modeling unit 146 uses a PKPD model to jointly estimate parameters of an equation that includes characteristics of both of these contributions. The patients to which the PKPD model is applied can be patients with the same type of cancer as the patients reflected in the PFS data or, in some cases, patients with types of cancer known to have very similar tumor growth characteristics.

[0056] As mentioned above, the techniques described herein may assume or apply any suitable type of growth curve (exponential, logistic, etc.). In some embodiments where exponential growth is assumed, the patient modeling unit 146 may jointly estimate tumor growth parameters for a particular patient using the following PKPD model:

number

[0057] The patient modeling unit 146 may learn the patient-specific parameters of Equation 4 (or the patient-specific distribution of the parameters of Equation 4) by attempting to fit Equation 4 to the patient's measured / observed tumor size / growth (i.e., over time and during a series of two or more patient encounters), subject to certain constraints. For example, if exponential growth is assumed, the ... g Using the identified population distribution of k in Eq. g As a more specific example, the patient modeling unit 146 may set constraints on k corresponding to a 90% credible interval in the population distribution. g upper and lower limits of k are identified, and then these values ​​are used to calculate the k for a particular patient. gmay be used as upper and lower limits when estimating

[0058] The patient modeling unit 146 may also use an informative prior to set constraints on one or more other parameters in Equation 4. For example, k max may have an informative prior distribution of 0.025 (e.g., about the mean of a log-normal distribution), as informed by the fastest responding patients in the population, but is allowed to vary from this value in the joint estimation process.

[0059] Once the patient modeling unit 146 has estimated the parameters and / or parameter distributions, the user interface unit 140 can cause a display (e.g., display 124) to present a visual representation of the estimated tumor growth for a particular patient in any suitable format. For example, for a particular patient, the user interface unit 140 can output the plot / information shown in any one of the columns shown in Figure 7, where each column represents a particular combination of drug dose (20 mg or 60 mg in this example) and cancer indication (testicular or colorectal in this example) for a particular patient.

[0060] In the top row of each column, each point represents the observed / measured concentration of drug in the plasma of each patient, and the solid line / trace represents the mean concentration in plasma estimated by the patient modeling unit 146 using a PKPD model similar to Equation 4. Although not shown in FIG. 7, shaded zones may be displayed around the solid line / trace (e.g., to represent a 90% confidence interval for the concentration in plasma). In the bottom row of each column, each point represents the observed / measured baseline-normalized SLD, and the top horizontal line indicates a baseline-normalized SLD value of 1.2. The bottom solid line / trace represents the mean estimated baseline-normalized SLD for each patient, and the bottom dashed line / trace represents the estimated baseline-normalized SLD for each patient in a counterfactual scenario where the drug had not been administered to the patient (i.e., the patient's estimated tumor growth in the absence of drug treatment). In the bottom row, the solid line / trace corresponds to T' in Equation 4, and the dashed line / trace corresponds to the first term on the right side of Equation 4. The shaded zones around the dashed lines represent the 90% confidence interval. Although not shown in FIG. 7, the solid line may have a shaded zone around it to represent the 90% confidence interval.

[0061] By showing a particular patient's tumor growth trajectory against the actual trajectory (i.e., against the real-world observed and / or estimated overall growth rate) versus what would have happened if the particular patient had not received drug treatment, Figure 7 can enable a user to accurately assess the effectiveness of a drug for the indicated cancer type at the indicated dose level. For example, a user may determine that in the case of 60 mg / colorectal, the low overall growth rate is due to the patient's low baseline tumor growth, which is far greater than the effectiveness of the drug / dose in that patient. On the other hand, in the case of 20 mg / testicular, a user may determine that the negative growth rate is primarily due to drug efficacy, given the positive baseline growth that would have otherwise occurred. Also, in the case of 60 mg / testicular, because the baseline growth rate is significantly higher than that growth rate, a user may determine that the drug is effective despite the rather high growth rate.

[0062] 8 is a flow diagram of an exemplary method 800 for estimating tumor growth. Method 800 may be performed by computing system 100 (e.g., processing unit 120), for example, when executing instructions of TGE application 130. In some embodiments, method 800 may include a Bayesian generative model.

[0063] Method 800 includes step 802, in which one or more processors (e.g., one or more processors of computing system 110) can obtain progression-free survival (PFS) data for a plurality of patients (e.g., from patient database 112 or local memory). Patients (or subjects) can include any living or non-living entity, including, but not limited to, humans (e.g., male humans, female humans, fetuses, pregnant women, children, etc.), non-human animals, plants, bacteria, fungi, or protozoans. Any human or non-human animal can serve as a patient, including, but not limited to, mammals, reptiles, birds, amphibians, fish, ungulates, ruminants, bovines (e.g., cows), equines (e.g., horses), caprines and ovines (e.g., sheep, goats), porcines (e.g., pigs), camelids (e.g., camels, llamas, alpacas), monkeys, apes (e.g., gorillas, chimpanzees), ursids (e.g., bears), poultry, dogs, cats, mice, rats, fish, dolphins, whales, and sharks. In some embodiments, the patient (or subject) is a male or female (e.g., a man, woman, or child) at any stage of development. The multiple patients may be patients associated with one or more drug treatments. The one or more drug treatments may include effective drug treatments (e.g., successful trials), neutral drug treatments, or ineffective drug treatments (e.g., failed trials). Details of the one or more drug treatments are described elsewhere herein.

[0064] Progression-free survival (PFS) may include the time from the start of treatment to the occurrence of disease progression or death. In some embodiments, disease progression can be assessed by Response Evaluation Criteria in Solid Tumors (RECST) as an increase in the sum of the largest tumor diameters of at least 20%, the development of any new lesions, or a clear increase in non-measurable malignant disease. In some embodiments, PFS may be used as an endpoint. Endpoints may include targeted outcomes of clinical trials to determine the efficacy and safety of the therapy being tested. Clinical trial endpoints may include one or more clinical outcome assessments and / or surrogate endpoints. In some embodiments, clinical outcome assessments may include cure, clinical deterioration, and mortality. Surrogate endpoints may be clinical trial endpoints used as a substitute for direct measures of how a patient feels, functions, or survives. PFS data may include any information related to PFS, including, but not limited to, PFS plots, digitized PFS plots, or PFS risk tables, as described elsewhere herein. PFS data may include published or unpublished PFS data. The PFS data can indicate the number of patients among a plurality of patients who have a baseline normalized sum longest diameter (SLD) measurement of at least 1.2 or who develop new lesions at each of a plurality of observation times and / or within a recent time window. The plurality of patients represented by the PFS data can include patients known to be associated with one or more drug treatments, as described elsewhere herein.

[0065] The PFS data can indicate (i) multiple observation times and / or (ii) the number of patients among multiple patients who experienced a PFS event at each of the multiple observation times. The multiple observation times can include any time range, for example, at least 1 month, 2 months, 3 months, 4 months, 5 months, 6 months, 1 year, 5 years, or more. In some embodiments, the multiple observation times can include any time range, for example, up to 5 years, 1 year, 6 months, 5 months, 4 months, 3 months, 2 months, 1 month, or less. The multiple observation times can be at least 1 hour, 1 day, 1 month, 3 months, 1 year, or more. In some other embodiments, the multiple observation times can be up to 1 year, 3 months, 1 month, 1 day, or less. PFS events may include, but are not limited to, progression of non-target lesions, an SLD observation in which the baseline-normalized SLD is 1.2 times greater than the smallest observed SLD, an SLD observation in which the baseline-normalized SLD is at least 5 mm greater than the smallest observed SLD, or any other event related to PFS, including, but not limited to, a situation in which a new lesion is present within a recent time window. The recent time window may be the same as or different from the multiple observation times. The recent time window may be at least 1 hour, 1 day, 1 month, 3 months, 1 year, or longer. In some other embodiments, the recent time window may be at most 1 year, 3 months, 1 month, 1 day, or less. The number of patients with PFS events at each of the multiple observation times may be at least 10, 100, 1,000, 10,000, or more. The number of patients with PFS events at each of the multiple observation times may be at most 10,000, 1,000, 100, 10, or less. In some embodiments, the PFS data may include how many patients had a PFS event in a subset of the plurality of observation times. The subset of the plurality of observation times may be at least 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, or more of the plurality of observation times. In some embodiments, the subset of the plurality of observation times may be up to 90%, 80%, 70%, 60%, 50%, 40%, 30%, 20%, 10%, or less of the plurality of observation times.The PFS data may correspond to one or more specific cancer types, including, but not limited to, breast cancer, colorectal cancer, esophageal cancer, head and neck cancer, lung cancer, lymphoma, ovarian cancer, pancreatic cancer, prostate cancer, renal cancer, or uterine cancer.

[0066] In step 804, the one or more processors can determine a population distribution of one or more patient-specific parameters of the growth curve function. The population distribution can include the distribution of one or more parameters or characteristics (e.g., patient-specific parameters) among multiple individuals in a population. The one or more parameters can include patient-specific parameters and non-patient-specific parameters (e.g., population parameters). The one or more patient-specific parameters can include tumor growth parameters, PKPD parameters, or growth curve parameters. The one or more patient-specific parameters can include individual parameters, SLD observations, or non-target progression events. The population parameters can be determined by a population, for example, chemotherapy-naive prostate cancer patients in a phase 3 trial of antiandrogen therapy. For example, in FIG. 9, the population parameters can include μ ∼ half-normal (0, 0.1) and τ ∼ half-normal (0, 1). The individual / patient-specific parameters can be plotted conditional on the population parameters. For example, as shown in FIG. 9, the individual / patient-specific parameters can be

number

[0067] In some embodiments, identifying a population distribution for one or more patient-specific parameters may include determining a growth curve function that includes the one or more patient-specific parameters. The growth curve function may include an exponential growth function, a logistic growth function, or an ordinary differential function. The growth curve function may include Equation 1, Equation 2, or Equation 3, as disclosed elsewhere herein. Details of growth curve functions are described elsewhere herein. The population distribution of the growth curve may be generalized in a probabilistic programming language. The growth curve function may be time-dependent. In this situation, the growth curve function may change based on multiple observation times. In some embodiments, the method may further include identifying, via one or more processors, the population distribution of the one or more parameters.

[0068] In some embodiments, the one or more patient-specific parameters may be, for example, θ i θ i The growth curve function associated with i ) In some embodiments, the growth curve function f(t,θ i ) of θ i where t represents time and i is an index representing the i-th patient among multiple patients. For example, if exponential growth is assumed, the patient-specific parameter θ i is the parameter k g and the growth curve function may be as shown in Equation 1. In some embodiments, the one or more patient-specific parameters may include:

number

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number

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[0069] In various embodiments, identifying population distributions for one or more patient-specific parameters may include identifying a single population distribution for a single patient-specific parameter, identifying respective population distributions for two or more patient-specific parameters, or identifying a single joint population distribution for two or more patient-specific parameters. The one or more patient-specific parameters may include a baseline normalized sum of longest diameters (SLD) measurement parameter. The baseline normalized SLD measurement may be determined based on PSF data. Details of the baseline normalized SLD measurement are described elsewhere herein. The one or more patient-specific parameters may include a growth rate parameter (e.g., a tumor proliferation parameter). The growth rate parameter may include a baseline growth rate parameter with or without treatment. The one or more patient-specific parameters may include a parameter related to the proportion of drug-sensitive tumor cells in a patient among the plurality of patients. The value of the parameter related to the proportion of drug-sensitive tumor cells in a patient among the plurality of patients ranges from 0 to 1. In some embodiments, the value of the parameter related to the proportion of drug-sensitive tumor cells in a patient of the plurality of patients can be at least 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90% or more, hi some embodiments, the value of the parameter related to the proportion of drug-sensitive tumor cells in a patient of the plurality of patients can be up to 90%, 80%, 70%, 60%, 50%, 40%, 30%, 20%, 10%, or less.

[0070] Identifying a population distribution for one or more patient-specific parameters may include fitting a growth curve function to observations at multiple observation times. Identifying one or more population distributions may include fitting a growth curve function to observations at a subset of the multiple observation times. The subset of the multiple observation times may be selected automatically via a mathematical model or manually by one or more users. For example, the observations may include, for each patient of the multiple patients, a first observation at a first time indicating that the patient did not have a PFS event before the first time, and a second observation at a second time indicating that the patient had a PFS event before the second time. The population distribution may include any type of distribution, including, but not limited to, a lognormal distribution, a Bernoulli distribution, a uniform distribution, a binomial distribution, a normal or Gaussian distribution, an exponential distribution, or a Poisson distribution.

[0071] In step 806, the one or more processors may obtain (e.g., from the patient database 112 or a local memory such as the memory 128) measured tumor growth data for a particular patient receiving drug therapy. The tumor growth data may include any information regarding tumor growth, for example, but not limited to, tumor diameter over time, tumor volume over time, or tumor growth rate. The tumor growth data may be obtained by any type of imaging technique, including mammography, ultrasound (US), and magnetic resonance imaging (MRI). The drug therapy may include one or more cancer therapeutic agents, for example, but not limited to, chemotherapeutic agents, targeted cancer therapeutic agents, differentiation therapy agents, hormonal therapy agents, and immunotherapeutic agents. For example, the therapy may be one or more chemotherapeutic agents selected from the group consisting of alkylating agents, antimetabolites, anthracyclines, antitumor antibiotics, cytoskeleton disrupting agents (taxanes), topoisomerase inhibitors, mitotic inhibitors, corticosteroids, kinase inhibitors, nucleotide analogs, platinum-based drugs, and any combination thereof. In some embodiments, the therapy is one or more targeted cancer therapy agents selected from the group consisting of signal transduction inhibitors (e.g., tyrosine kinase and growth factor receptor inhibitors), histone deacetylase (HDAC) inhibitors, retinoic receptor agonists, proteosome inhibitors, angiogenesis inhibitors, and monoclonal antibody conjugates. In some embodiments, the therapy is one or more differentiation therapy agents, including retinoids such as tretinoin, alitretinoin, and bexarotene. In some embodiments, the therapy is one or more hormonal therapy agents, including antiestrogens, aromatase inhibitors, progestins, estrogens, antiandrogens, and GnRH agonists or analogs. In one embodiment, the therapy is one or more immunotherapy agents, including monoclonal antibody therapy.

[0072] In step 808, the one or more processors may estimate tumor growth for a particular patient (e.g., a patient having the same cancer type as the plurality of patients) based on (i) the measured tumor growth data and (ii) the identified population distribution. Step 808 may include modeling the tumor growth rate for the particular patient using a PKPD model (e.g., Equation 4 or similar) having a first term representing tumor size change in the particular patient without drug treatment and a second term representing the contribution of drug treatment to tumor size change in the particular patient, and jointly estimating one or more parameters of the first term and one or more parameters of the second term by fitting the PKPD model to the measured tumor growth data. The joint estimation may involve using the population distribution identified in block 804 to impose constraints on one or more parameters of the first term (e.g., k g The parameters of the second term may include, for example, the drug concentration in the patient's plasma, the patient's k max (maximum mortality), and / or half-maximal effective concentration (EC50). Constraints may include any population prior distribution.

[0073] Estimating tumor growth may further include obtaining an overall response rate (ORR) for a particular patient receiving drug treatment. The ORR may include the number of patients experiencing a response. A response may include the observation that a patient's tumor growth meets one or more response conditions. A response condition may include the patient's tumor size being less than 0.7 times the baseline SLD (or 30% less than the patient's baseline SLD). In some embodiments, the ORR is calculated for each sample and can be fixed at a single value. For example, the exact inference can be summed over all possible combinations of responders. Alternatively, this can be approximated by setting the proportion of simulated responders close to the observed one:

number

[0074] Estimating tumor growth may further include obtaining one or more non-target progression events for a particular patient receiving drug treatment. In situations where progression is not due to SLD reaching a specific threshold, non-target progression events such as the appearance of new lesions, progression of non-target lesions, symptomatic worsening, or death can be included in the population distribution or growth curve to determine tumor growth. One or more non-target progression events can be included by modeling the time to these non-target events using a hazard function. The hazard function may include a function of tumor growth inhibition kinetics. In some embodiments, the PFS data corresponds to a particular cancer type, and estimating tumor growth for a particular patient may include estimating tumor growth for patients diagnosed with a particular cancer type.

[0075] In step 812, the one or more processors may cause a display (e.g., display 124) to present a visual representation of the estimated tumor growth for a particular patient. Step 812 may include, for example, generating and / or inputting a user interface. In some embodiments, step 812 includes causing the display to display a tumor growth trajectory for a particular patient if the particular patient had not received any drug treatments. In this situation, the visual representation of the estimated tumor may be presented to a health / research professional on the user interface, and the health / research professional may prescribe one or more drug treatments. In some other embodiments, step 812 includes causing the display to display a tumor growth trajectory for a particular patient if the particular patient had received one or more drug treatments. In this situation, the visual representation of the estimated tumor may be presented to a health / research professional on the user interface, and the health / research professional may adjust the dose, regimen, or anti-drug antibodies associated with one or more drug treatments. In this situation, such changes in the dose, regimen, or anti-drug antibodies associated with one or more drug treatments may be displayed to the patient via the one or more processors.

[0076] The methods and systems disclosed herein may further include adjusting the dose of a drug therapy based on the estimated tumor growth of a particular patient. For example, if the tumor growth of a particular patient is lower than a predetermined threshold (e.g., a predetermined tumor growth rate), the dose of the drug therapy may be adjusted to a lower dose. In another example, if the tumor growth of a particular patient is higher than a predetermined threshold, the dose of the drug therapy may be adjusted to a higher dose. Additionally, in some embodiments, the estimated tumor growth of a particular patient can be used to evaluate the effectiveness of a drug therapy, evaluate the effectiveness of a combination of one or more drug therapies, or compare the direct results of each drug therapy as a monotherapy and as a combination of one or more drug therapies.

[0077] Additional considerations regarding the present disclosure are now provided.

[0078] Some of the figures described herein show example block diagrams having one or more functional components. It will be understood that such block diagrams are for illustrative purposes and that the devices described and shown may have more, fewer, or alternative elements than those shown. Furthermore, in various embodiments, the components (and the functionality provided by each component) may be associated or integrated as part of any suitable component.

[0079] Embodiments of the present disclosure relate to non-transitory computer-readable storage media having computer code for performing various computer-implemented operations. As used herein, the term "computer-readable storage medium" includes any medium capable of storing or encoding a sequence of instructions or computer code for performing the operations, techniques, and methods described herein. The medium and computer code may be those specially designed and constructed for embodiments of the present disclosure, or may be of the kind well known and available to those skilled in the computer software arts. Examples of computer-readable storage media include, but are not limited to, magnetic media such as hard disks, floppy disks, and magnetic tape; optical media such as CD-ROMs and holographic devices; magneto-optical media such as optical disks; and hardware devices specially configured to store and execute program code, such as ASICs, programmable logic devices ("PLDs"), and ROM and RAM devices.

[0080] Examples of computer code include machine code, such as produced by a compiler, and files containing high-level code executed by a computer using an interpreter or compiler. For example, embodiments of the present disclosure may be implemented using Java, C++, or other object-oriented programming languages ​​and development tools. Further examples of computer code include encrypted code and compressed code. Furthermore, embodiments of the present disclosure may be downloaded as a computer program product, which may be transferred from a remote computer (e.g., a server computer) to a requesting computer (e.g., a client computer or a different server computer) over a transmission channel. Other embodiments of the present disclosure may be implemented in hardwired circuitry in place of or in combination with machine-executable software instructions. [Example]

[0081] Bayesian generative model of published PFS and ORR data Methods and systems disclosed herein have been developed to estimate tumor growth. In some embodiments, a Bayesian generative model was developed that specifies the joint distribution of one or more parameters, including study-specific parameters, group-specific parameters, individual patient parameters, individual SLD observations, non-target progression events, and PFS and ORR reported in published studies. The model included a semi-mechanistic population component to capture longitudinal tumor dynamics at the individual and population levels. Furthermore, the model included a novel component based on RECIST criteria that specifies the distribution of individual time to progression and response, conditional on individual tumor dynamics. RECIST criteria were the criteria for determining whether a tumor disappeared, shrank, stayed the same, or grew, including complete response (CR), partial response (PR), stable disease (SD), and progressive disease (PD). The joint distribution allowed for the joint estimation of one or more parameters conditional on observational data from published studies using standard Bayesian estimation.

[0082] Individual tumor kinetics was described using a standard two-state model representing two tumor subpopulations, each with linear growth and death:

number

[0083] where R1 is a parameter that describes the subpopulation of drug-sensitive cells, and R2 is the death rate k kkillr <k kkill represents a subpopulation of more resistant cells (e.g., drug-insensitive cells) where k kkillr is the death rate of more resistant cells, and k kkill is the death rate of drug-sensitive cells). The baseline growth rate is k g The subpopulations were associated with the proportion of drug-sensitive tumor cells in the patient among the patients. The overall tumor burden / function R(t) was equal to the weighted sum of R1(t) and R2(t) with parameter f determining the proportion of drug-sensitive tumor cells in the patient among the patients and the proportion of drug-insensitive tumor cells in the patient among the patients. The linear model therefore allows the following closed-form solution in conventional bi-exponential form:

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[0084] The initial SLD, proliferation rate, and drug-sensitive cell proportion were individual-specific parameters (or patient-specific parameters) and were distributed according to the following distribution for patients in the same study, regardless of group:

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[0085] SLD observation X at time t t Patient-specific parameters: X t ~LogNormal(R(t),σ) The distribution was modeled as a log-normal distribution for R(t) subject to

[0086] The time to event for non-target progression events, N, which is the time to progression of non-target lesions or appearance of new lesions according to RECIST criteria, was modeled conditional on patient-specific parameters via a hazard model based on: h(t)=exp{λ0+λ1R(t)+λ2R'(t)}.

[0087] Hazard was modeled to be proportional to both the absolute tumor burden or growth rate and its rate of change. This captured the situation where the dynamics of non-target lesions are correlated with target lesions, and the appearance of new lesions is intuitively more likely when the existing tumor burden is large and growing. The parameters σ and λ could not be identified from the PFS and ORR data alone, but their values, or at least a prior distribution of their values, were obtained by fitting the model to actual SLD data, which were often not publicly available. The parameters were set to the following fixed values, obtained from point estimates of model fitting to private SLD data from an internal program: σ = 0.1, λ = -6.4, λ = 0.05. 2=0.014, λ2 = 2.6. For values ​​of λ, all parameters were found to be significant in the sense that at least 90% of the posterior masses were far from zero.

[0088] As shown in Figure 9, a patient's last observation time and whether they had progressed at that time were captured by a tuple (T, E). This quantity was modeled conditional on a vector containing one or more patient SLD measurements, denoted X, and a non-target progression event time, N. T is set to the patient's last observation time. E was determined conditional on X and N according to RECIST criteria. For example, if E=1, progression occurred at T=1 when the patient had either target or non-target progression at time T. A non-target progression event occurred at time T when N=T by definition, but the relationship between target progression and X was slightly more complex. According to RECIST, target progression occurs when X T is 1.2 times the smallest observed value of X by time T and / or X T also occurred at time T if was at least 5 mm greater than the observed minimum. <Tについて、X t is below this threshold, target progression did not occur earlier. This was expressed as the following inequality holding:

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[0089] Similarly, if a patient drops out without progressing at time T, or more specifically, if N>T and all X up to and including time T are below the aforementioned threshold, then E=0. Bayesian inference data (T, E) are conditional, or held fixed, and the values ​​of the unknown quantities X and N that account for fixation (T, E) were estimated by Bayes' rule, in this case Markov Chain Monte Carlo (MCMC) sampling. To capture right-censoring in published studies, dropout was treated as the time to event that occurred at time T, where E=0. This was modeled using a group-specific hazard constant d.

[0090] Whether a patient experienced any response and whether a patient experienced a complete response were captured by the tuple (O,C). Similar to progression time and status, this quantity was also modeled conditionally on X and N. X t If the minimum value of is less than 0.7R0 and no non-target progression events have occurred up to and including that time point, set O to 1; otherwise, set O to 0. t If the smallest value of X was less than 2 mm, C, indicating a complete response, was set to 1. A complete response is described in the RECIST criteria as the complete disappearance of all lesions, but this boundary was chosen for two reasons. First, numerically, X t The minimum value of is a positive number, and therefore a realistic threshold was chosen. Second, it was a practically small enough value that disappeared lesions would no longer be spotted on imaging.

[0091] The entire data generation process, i.e., joint distribution structure, is specified in Figure 9. It is summarized by the following joint distributions for data and parameters:

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[0092] In Figure 9, the bottom left plot shows that individual-specific parameters have a significant impact on potential tumor dynamics. The bottom center plot shows how potential X and N observations relate to actual potential SLD observations. The bottom right table shows how the set of random variables T, E, O, and C relate to the published actual PFS and ORR.

[0093] Bayesian inference of model parameters given observed data Inference of model parameters was performed using standard Bayesian inversion of the data generation process facilitated by MCMC posterior sampling. Specifically, prior distributions for the model parameters were specified and multiplied by the conditional distributions described above to obtain a joint distribution over the model parameters and the observed data. The observed data were then fixed to the observed values, e.g., adjusting the conditions, and the resulting non-normalized posterior densities of the model parameters were sampled using MCMC.

[0094] For most parameters, prior distributions were set to allow a wide range of plausible values ​​that would allow the model to explain the various example data from published studies shown in the Results section, while also reducing the likelihood of unrealistic and numerically unstable values. Specifically, several parameters were chosen to be kg ~HalfNormal(0,0.1) and k kkill ~HalfNormal(0,0.02). The latter allows k to be calculated while avoiding the fast mortality that leads to numerical instabilities in the hazard integration. kkill We set the pre-mass to a reasonable value of . Meanwhile, k kkillr The ~Exponential(1000) served two purposes. First, it placed a significant amount of pre-mass at zero, which meant that the growth kinetics of the more resistant cells in the control / placebo group were k g This facilitated the complete determination of the k kkillr This helped with the identifiability problem without having to explicitly set k to zero. Second, the exponential distribution had heavy tails, which allowed for a faster mortality rate k s The study largely captured early responses rather than longer-term progression, allowing for sufficient flexibility to better capture any long-term benefits that treatment may have over control or placebo. f We tried a fixed value of 0, which corresponds to f=0.5. However, a more relaxed μ f It was found that ~N(0,0.5) actually yielded a better fit, while still encouraging the SLD trajectory to maintain the characteristic biexponential U shape commonly found in practice. The priors for the dispersion parameters are

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[0095] Observed data (e.g., PFS data) were extracted from published studies, including PFS curves and risk tables, ORR, and the number of complete responders, and as much information as possible was incorporated into the model. The standard Kaplan-Meier formula was used to combine the risk table and PFS curve, and at each time point τ in the risk table, the number of patients who progressed and dropped out at that time point, M, were calculated. τ1 and M τ0 The likelihood of progression data was then set according to the following formula:

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[0096] Information about the number of overall and complete responders (e.g., patients who responded to treatment) was incorporated slightly differently into the likelihood. Published studies generally specified the number of overall and complete responders, but did not specify which patients were responders, and therefore, O τ·i and C τ·i The value of was unknown. Nevertheless, the flexibility of probabilistic programming languages ​​such as Stan allowed us to condition this information on the joint probability density. The number of observed total and complete responders was

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[0097] Simulated Data To demonstrate the model's ability to retrieve tumor kinetics using PFS and ORR information, a simulated dataset with known ground truth parameter values ​​was simulated and back-estimated. The population-level growth kinetic parameters shared between groups were calculated as:

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[0098] Figure 10 shows several posterior draws of the SLD (e.g., X) of a single patient from the control group who progressed at the second post-baseline scan, with the ground truth values ​​overlaid in red. Conditioning on this information would impose constraints on X, resulting in posterior draws from the space of possible SLD values ​​that could plausibly have led to the patient's progression at the second post-baseline scan. X had a joint posterior distribution that also depended on other parameters not shown here, such as R and N. For example, some draws showed a decline in SLD over time, which was consistent with the fact that this patient had progression, as would be the case if the patient's progression was explained by non-target progression.

[0099] Figure 11 summarizes, for each patient, the marginal posterior values ​​estimated from the model along with the ground truth values. The top and middle subfigures show the k values ​​for each patient. g Marginal posterior median and 90% credible intervals for the and f parameters are shown. Ground truth values ​​are overlaid, demonstrating good posterior coverage of the true parameter values. The estimates for each patient were plotted by the patient's progression or dropout time, T, and two notable patterns emerged. First, the later the patient's known progression time, the larger the posterior weights, as expected, corresponding to larger k gand f values ​​were given. Second, the model could estimate a patient's progression or dropout time T and whether the patient actually progressed at that time E, but not their actual SLD measurements. Therefore, patients with identical T and E values ​​had identical posterior distributions for individual parameters. The bottom two subfigures of Figure 11 show the marginal posterior probability that each individual patient is one of the responders, with the actual ground truth responders depicted as dotted lines. As mentioned above, the number of responders is known, not which patients are responders; therefore, in each posterior sample, different combinations of patients formed the responder group. Intuitively, patients who progressed later were more likely to belong to this group, which was captured by the model in terms of higher posterior probabilities.

[0100] Figure 12 shows the posterior draws of test- and group-specific parameters with their ground truth values ​​overlaid (k killr (Note that parameters were omitted due to space constraints.) The posterior distributions showed good coverage of ground truth values ​​and demonstrated the model's ability to capture population-level dynamics using PFS and ORR summary information. Pair plots also reflected the complex nonlinear relationships between the dynamic parameters captured by the posterior distributions. For example,

number

[0101] Published research To demonstrate the model's ability to capture tumor dynamics information from published studies, we applied this method to three published studies in metastatic castration-resistant prostate cancer (mCRPC). These studies are summarized in Table 1. All models were fitted until the R value for all parameters was less than 1.05, following standard guidance. To assess the fit of the model to the published data, a posterior predictive check (PPC) was performed, in which each arm of the study was drawn conditional on each posterior draw of the population-level parameters, and all new values ​​of the individual-level parameters R, K were calculated. g , f. The entire data generation process was then simulated once for each posterior draw to obtain the PFS curve and the total number of responses at each draw. These simulated values ​​were then overlaid with the observed values ​​in the PPC to assess the adequacy of the fit. The resulting plot is shown in Figure 13. Although ground truth values ​​were not available for any of the population-level, individual-level, or SLD parameters, the model demonstrated excellent ability to capture the observed PFS curves and response data across various published studies.

[0102] [Table 1]

[0103] Simulation of novel test conditions using published research The posterior estimates from two different published studies from the previous subsection were combined in an in silico study to 1) evaluate the efficacy of the drug treatments tested in post-chemotherapy patients in the chemotherapy-naive setting; 2) evaluate the efficacy of combinations of one or more drug treatments; and 3) compare the direct results of each drug treatment as monotherapy and in combinations of one or more drug treatments.

[0104] Four groups with 500 patients each comprised 100 participants from the general study from the previous subsection that was conducted in a chemotherapy-naive setting (e.g., patients not treated with chemotherapy).

number

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[0105] We introduced a Bayesian generative model that combines published PFS and response data with tumor dynamics. This model allowed us to estimate important tumor dynamic parameters and information using publicly available data. Several results were demonstrated. First, an example using simulated data for which the ground truth was known was presented to demonstrate the model's ability to retrieve tumor dynamic parameters using published data. Second, we applied the model and demonstrated good fit to three published studies from actual mCRPC trials. Finally, we combined these estimated parameter values ​​to compare these therapies in an in silico study under a novel trial setting and in combination with each other.

[0106] One exemplary implementation of a computer system 1500 that may be used in connection with any of the embodiments of the technology described herein is shown in FIG. 15. The computer system 1500 includes one or more processors 1510 and one or more articles of manufacture that include non-transitory computer-readable storage media (e.g., memory 1520 and one or more non-volatile storage media 1530). The processor 1510 may control the writing of data to and reading of data from the memory 1520 and non-volatile storage media 1530 in any suitable manner, as aspects of the technology described herein are not limited to any particular technology for writing or reading data. To perform any of the functions described herein, the processor 1510 may execute one or more processor-executable instructions stored in one or more non-transitory computer-readable storage media (e.g., memory 1520), which function as non-transitory computer-readable storage media that store the processor-executable instructions executed by the processor 1510.

[0107] Computer system 1500 may also include a network input / output (I / O) interface 1540 that allows the computing device to communicate with other computing devices (e.g., over a network), and may also include one or more user I / O interfaces 1550 that allow the computing device to provide output to and receive input from a user. User I / O interfaces may include devices such as a keyboard, a mouse, a microphone, a display device (e.g., a monitor or touchscreen), speakers, a camera, and / or various other types of I / O devices.

[0108] The above-described embodiments can be implemented in a variety of ways. For example, the embodiments may be implemented using hardware, software, or a combination thereof. If implemented in software, the software code may be executed on any suitable processor (e.g., a microprocessor) or collection of processors, whether provided on a single computing device or distributed across multiple computing devices. It should be understood that any component or collection of components that perform the functions described above can be generally thought of as one or more controllers that control the functions described above. The one or more controllers can be implemented in a variety of ways, such as dedicated hardware or general-purpose hardware (e.g., one or more processors) that are programmed using microcode or software to perform the functions described above.

[0109] In this regard, it should be understood that one implementation of the embodiments described herein includes at least one computer-readable storage medium (e.g., RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile disk (DVD) or other optical disk storage, magnetic cassette, magnetic tape, magnetic disk storage or other magnetic storage device, or other tangible, non-transitory computer-readable storage medium) encoded with a computer program (i.e., a plurality of executable instructions) that, when executed on one or more processors, performs the above-described functions of one or more embodiments. The computer-readable medium may be transportable such that a program stored thereon may be loaded into any computing device to implement aspects of the technology described herein. Furthermore, it should be understood that reference to a computer program that, when executed, performs any of the above-described functions is not limited to an application program running on a host computer. Rather, the terms computer program and software are used herein in a generic sense to refer to any type of computer code (e.g., application software, firmware, microcode, or any other form of computer instructions) that can be used to program one or more processors to implement aspects of the technology described herein.

[0110] The foregoing description of implementations has been provided for illustration and description, and is not intended to be exhaustive or to limit the implementations to the precise forms disclosed. Modifications and variations are possible in light of the above teachings or may be acquired from practice of the implementations. In other embodiments, the methods depicted in these figures may include fewer operations, different operations, operations in a different order, and / or additional operations. Moreover, non-dependent blocks may be performed in parallel.

[0111] It will be understood that the exemplary aspects as described above may be implemented in various forms of software, firmware, and hardware in the implementations shown in the figures. Furthermore, certain portions of the implementation may be implemented as a "module" that performs one or more functions. The module may include hardware, such as a processor, an application specific integrated circuit (ASIC), or a field programmable gate array (FPGA), or a combination of hardware and software.

[0112] While several aspects and embodiments of the technology described in this disclosure have been described, it will be understood that various alterations, modifications, and improvements will readily occur to those skilled in the art. It is intended that such alterations, modifications, and improvements be made within the spirit and scope of the technology described herein. For example, those skilled in the art will readily envision numerous other means and / or structures for performing the functions and / or obtaining the results and / or one or more advantages described herein, and each such variation and / or modification is deemed to be within the scope of the embodiments described herein. Those skilled in the art will recognize or be able to ascertain using no more than routine experimentation many equivalents to the specific embodiments described herein. Accordingly, the foregoing embodiments are presented by way of example only, and it will be understood that, within the scope of the appended claims and their equivalents, embodiments of the invention may be practiced otherwise than as specifically described. Furthermore, any combination of two or more features, systems, articles, materials, kits, and / or methods described herein is within the scope of the present disclosure, unless such features, systems, articles, materials, kits, and / or methods are mutually inconsistent.

[0113] The above-described embodiments may be implemented in a variety of ways. One or more aspects and embodiments of the present disclosure involving the performance of a process or method utilize program instructions executable by a device (e.g., a computer, processor, or other device) to perform or control the performance of the process or method. In this regard, various inventive concepts may be embodied as a computer-readable storage medium (or multiple computer-readable storage media) (e.g., computer memory, one or more floppy disks, compact disks, optical disks, magnetic tapes, flash memory, circuitry in field programmable gate arrays or other semiconductor devices, or other tangible computer storage media) encoded with one or more programs that, when executed on one or more computers or other processors, perform methods that implement one or more of the various embodiments described above. The computer-readable medium may be transportable, allowing the program stored thereon to be loaded onto one or more different computers or other processors to implement the various aspects described above. In some embodiments, the computer-readable medium may be non-transitory.

[0114] As used herein, the terms "program" or "software" are used generically to refer to any type of computer code or set of computer-executable instructions that can be used to program a computer or other processor to implement various aspects as described above. It will be further understood that, according to one aspect, one or more computer programs that, when executed, perform the methods of the present disclosure need not reside on a single computer or processor, but may be distributed in a modular manner among several different computers or processors to implement various aspects of the present disclosure.

[0115] Computer-executable instructions may be in many forms, such as program modules, executed by one or more computers or other devices. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform particular tasks or implement particular abstract data types. Typically, the functionality of the program modules may be combined or distributed as desired in various embodiments.

[0116] Additionally, the data structure may be stored in any suitable format on a computer-readable medium. For ease of explanation, the data structure may be depicted as having fields that are related by their location within the data structure. Such relationships may equally be achieved by assigning storage to the fields at locations within the computer-readable medium that convey the relationship between the fields. However, any suitable mechanism may be used to establish the relationship between information within the fields of the data structure, including the use of pointers, tags, or other mechanisms for establishing relationships between data elements.

[0117] When implemented in software, the software code may be executed on any suitable processor or collection of processors, whether provided on a single computer or distributed across multiple computers.

[0118] A computer may also have one or more input and output devices. These devices may be used, among other things, to display a user interface. Examples of output devices that may be used to provide a user interface include a printer or display screen for visually displaying output, and a speaker or other sound-generating device for audibly displaying output. Examples of input devices that may be used for a user interface include a keyboard and a pointing device such as a mouse, touchpad, or digital tablet. As another example, a computer may receive input information through speech recognition or other audio formats.

[0119] Such computers may be interconnected by one or more networks of any suitable form, such as a local area network or a wide area network such as an enterprise network, an intelligent network (IN), or the Internet, etc. Such networks may be based on any suitable technology and operate according to any suitable protocol, and may include wireless networks, wired networks, or fiber optic networks.

[0120] Also, as described, some aspects may be embodied as one or more methods. The actions performed as part of a method may be ordered in any suitable manner. Thus, embodiments may be constructed in which actions are performed in an order different from that shown, which may include performing some actions simultaneously even though shown as sequential actions in an exemplary embodiment.

[0121] As used herein, the singular terms "a," "an," and "the" can include plural referents unless the context clearly dictates otherwise.

[0122] As used herein, the terms "connect," "connected," and "connection" refer to an operable coupling or linking. Connected components may be directly coupled to each other or may be indirectly coupled, for example, through another set of components.

[0123] The term "and / or," as used in the specification and claims, should be understood to mean "either or both" of the elements so conjoined, i.e., elements that are present conjunctively in some cases and disjunctively in other cases. Multiple elements listed with "and / or" should be construed in the same manner, i.e., "one or more" of the elements so conjoined. Other elements may optionally be present other than the elements specifically identified in the "and / or" clause, whether related to those specifically identified elements or not. Thus, as a non-limiting example, a reference to "A and / or B," when used in conjunction with open-ended language such as "comprising," can, in one embodiment, refer to A only (optionally including elements other than B); in another embodiment, refer to B only (optionally including elements other than A); in yet another embodiment, refer to both A and B (optionally including other elements); and so forth.

[0124] As used herein and in the claims, the phrase "at least one" when used in reference to a list of one or more elements should be understood to mean at least one element selected from any one or more elements in the list of elements, but not necessarily including at least one of each element specifically set forth in the list of elements, and not excluding any combination of elements in the list of elements. This definition also allows for the optional presence of elements other than those specifically identified in the list of elements to which the phrase "at least one" refers, whether related to the specifically identified elements or not. Thus, as a non-limiting example, "at least one of A and B" (or, equivalently, "at least one of A or B" or, equivalently, "at least one of A and / or B") can refer in one embodiment to at least one (optionally including multiple) A's in the absence of B (and optionally including elements other than B); in another embodiment to at least one (optionally including multiple) B's in the absence of A (and optionally including elements other than A); in yet another embodiment to at least one (optionally including multiple) A's and at least one (optionally including multiple) B's (and optionally including other elements); etc.

[0125] In the claims and the above specification, all transitional phrases such as "comprising," "including," "carrying," "having," "containing," "involving," "holding," "consisting of," and the like, are understood to be open-ended, i.e., meaning including but not limited to. Only the transitional phrases "consisting of" and "consisting essentially of" shall be closed or semi-closed transitional phrases, respectively.

[0126] As used herein, the terms "approximately," "substantially," "substantial," and "about" are used to describe and account for slight variations. When used in conjunction with an event or circumstance, these terms can mean that the event or circumstance occurs precisely or that the event or circumstance occurs to a close approximation. For example, when used in conjunction with a numerical value, these terms can refer to a range of variation of ±10% or less of that numerical value, e.g., ±5% or less, ±4% or less, ±3% or less, ±2% or less, ±1% or less, ±0.5% or less, ±0.1% or less, or ±0.05% or less. For example, two numerical values ​​can be considered "substantially" the same if the difference between them is ±10% or less of the mean of those values, e.g., ±5% or less, ±4% or less, ±3% or less, ±2% or less, ±1% or less, ±0.5% or less, ±0.1% or less, or ±0.05% or less.

[0127] Furthermore, amounts, ratios, and other numerical values ​​may be presented herein in a range format. It should be understood that such range format is used for convenience and brevity and should be interpreted flexibly to include the numerical values ​​stated as the limits of the range, but also to include every individual numerical value or subrange subsumed within that range, as if each numerical value and subrange were expressly stated.

[0128] While the present disclosure has been described and illustrated with reference to specific embodiments thereof, such description and illustration are not intended to limit the disclosure. Those skilled in the art should understand that various changes may be made and equivalents may be substituted without departing from the true spirit and scope of the present disclosure, as defined by the appended claims. The figures may not be drawn to scale. Differences between the artistic representations in this disclosure and the actual devices may occur due to manufacturing processes, tolerances, and / or other reasons. There may be other embodiments of the disclosure not specifically illustrated. The specification and drawings (other than as claimed) are to be considered illustrative rather than restrictive. Changes may be made to adapt a particular situation, material, composition of matter, technique, or process to the objective, concept, and scope of the present disclosure. All such modifications are intended to be within the scope of the claims appended hereto. While the techniques disclosed herein have been described with reference to particular operations performed in a particular order, it will be understood that these operations may be combined, sub-divided, or rearranged to form equivalent techniques without departing from the teachings of the present disclosure. Thus, unless expressly stated herein, the order and grouping of the operations is not intended to be a limitation of the present disclosure.

Claims

1. 1. A computer-implemented method for estimating tumor growth, comprising: obtaining, by one or more processors, progression-free survival (PFS) data for a plurality of patients, the PFS data indicating (i) a plurality of observation times and (ii) at each of the plurality of observation times, a number of patients among the plurality of patients who experienced a PFS event within a most recent time window; determining, by the one or more processors, a population distribution of one or more patient-specific parameters based on the PFS data; obtaining, by the one or more processors, measured tumor growth data for a particular patient receiving drug treatment; and (ii) estimating, by the one or more processors, tumor growth for the particular patient based on (i) the measured tumor growth data and (ii) the population distribution of the one or more patient-specific parameters. causing the one or more processors to present on a display a visual representation of the estimated tumor growth for the particular patient; A method comprising:

2. The computer-implemented method of claim 1 , wherein identifying the population distribution of the one or more patient-specific parameters comprises determining a growth curve function that includes the one or more patient-specific parameters.

3. The computer-implemented method of claim 2 , wherein the growth curve function comprises at least one of an exponential growth function, a logistic growth function, or an ordinary differential function.

4. The computer-implemented method of any one of claims 1 to 3, wherein the one or more patient-specific parameters include a baseline normalized sum of longest diameter (SLD) measurement parameter.

5. The computer-implemented method of any one of claims 1 to 4, wherein the one or more patient-specific parameters include a growth rate parameter.

6. The computer-implemented method of claim 5 , wherein the growth rate parameters include baseline growth rate parameters without treatment.

7. The computer-implemented method of any one of claims 1 to 6, wherein the one or more patient-specific parameters include a parameter related to a proportion of drug-sensitive tumor cells in a patient of the plurality of patients.

8. 8. The computer-implemented method of claim 7, wherein the value of the parameter related to the proportion of drug-sensitive tumor cells in the patient of the plurality of patients ranges from 0 to 1.

9. The computer-implemented method of claim 2 , wherein the growth curve function is time-dependent.

10. The computer-implemented method of claim 2 , wherein determining the population distribution of the one or more patient-specific parameters comprises fitting the growth curve function to observations at the multiple observation time points.

11. The computer-implemented method of claim 3 , wherein the growth curve function is a logistic growth function, and the one or more patient-specific parameters include a plurality of parameters of the logistic growth function.

12. estimating tumor growth for the particular patient includes: modeling the tumor growth rate of the particular patient using a pharmacokinetic-pharmacodynamic (PKPD) model having a first term representing the change in tumor size in the particular patient not receiving the drug treatment and a second term representing the contribution to the change in tumor size in the particular patient due to the drug treatment; jointly estimating one or more parameters of the first term and one or more parameters of the second term by fitting the PKPD model to the measured tumor growth data, in part by setting constraints on the one or more parameters of the first term using the population distributions of the one or more patient-specific parameters; The computer-implemented method of any one of claims 1 to 11, comprising:

13. The one or more parameters of the second term are: the concentration of the drug in the plasma of said particular patient; the maximum mortality rate of said particular patient; and Half effective concentration (EC50) 13. The computer-implemented method of claim 12, comprising one or more of:

14. 14. The computer-implemented method of claim 1, wherein estimating the tumor growth further comprises obtaining an overall response rate for the particular patient receiving the drug treatment.

15. 15. The computer-implemented method of claim 1, wherein estimating the tumor growth further comprises obtaining one or more non-target events for the particular patient receiving the drug treatment.

16. 11. The computer-implemented method of claim 10, wherein the observations include, for each patient of the plurality of patients, a first observation at the first time indicating that the patient did not have a PFS event before the first time and a second observation at the second time indicating that the patient had a PFS event before the second time.

17. 17. The computer-implemented method of claim 1, wherein the PFS data corresponds to a particular cancer type, and wherein estimating tumor growth for a particular patient comprises estimating tumor growth for a patient diagnosed with the particular cancer type.

18. 18. The computer-implemented method of claim 1, wherein causing the display to present the visual representation of the estimated tumor growth for the particular patient comprises causing the display to display a trajectory of tumor growth for the particular patient if the particular patient had not received the drug treatment.

19. The computer-implemented method of any one of claims 1 to 18, wherein the population distribution for the one or more patient-specific parameters comprises a log-normal distribution.

20. 20. The computer-implemented method of any one of claims 1 to 19, wherein the PFS data comprises at least one of a digitized PFS plot or a PFS risk table.

21. 21. The computer-implemented method of any one of claims 1 to 20, wherein the PFS data indicates the number of patients among the plurality of patients who had a baseline normalized sum longest diameter (SLD) measurement of at least 1.2 or who developed new lesions at each of the plurality of observation times and within the most recent time window.

22. 22. The computer-implemented method of any one of claims 1 to 21, wherein the plurality of patients represented by the PFS data are patients associated with ineffective drug treatment.

23. 23. The computer-implemented method of any one of claims 1 to 22, further comprising adjusting the dose of the drug treatment based on the estimated tumor growth for the particular patient.

24. 1. A computer system for estimating tumor growth, comprising: a data storage device storing processor readable instructions; a processor configured to execute the instructions to perform the method; wherein the method comprises: obtaining progression-free survival (PFS) data for a plurality of patients, the PFS data indicating (i) a plurality of observation times and (ii) at each of the plurality of observation times, a number of patients among the plurality of patients who experienced a PFS event within a most recent time window; determining a population distribution of one or more patient-specific parameters based on the PFS data; Obtaining measured tumor growth data for a particular patient receiving drug treatment; (i) estimating tumor growth for the particular patient based on the measured tumor growth data and (ii) the population distribution of the one or more patient-specific parameters; causing a display to present a visual representation of the estimated tumor growth for the particular patient; 2. A computer system comprising:

25. 25. The computer system of claim 24, wherein identifying the population distribution of the one or more patient-specific parameters comprises determining a growth curve function that includes the one or more patient-specific parameters.

26. 26. The computer system of claim 25, wherein the growth curve function comprises at least one of an exponential growth function, a logistic growth function, or an ordinary differential function.

27. The computer system of any one of claims 24 to 26, wherein the one or more patient-specific parameters include a baseline normalized sum of longest diameter (SLD) measurement parameter.

28. The computer system of any one of claims 24 to 27, wherein the one or more patient-specific parameters include a growth rate parameter.

29. 30. The computer system of claim 28, wherein the growth rate parameters include baseline growth rate parameters without treatment.

30. 30. The computer system of any one of claims 24 to 29, wherein the one or more patient-specific parameters include a parameter related to a proportion of drug-sensitive tumor cells in a patient of the plurality of patients.

31. 31. The computer system of claim 30, wherein the value of the parameter relating to the proportion of drug-sensitive tumor cells in the patient of the plurality of patients ranges from 0 to 1.

32. 26. The computer system of claim 25, wherein the growth curve function is time dependent.

33. 26. The computer system of claim 25, wherein determining the population distribution of the one or more patient-specific parameters comprises fitting the growth curve function to observations at the multiple observation time points.

34. 27. The computer system of claim 26, wherein the growth curve function is a logistic growth function and the one or more patient-specific parameters include a plurality of parameters of the logistic growth function.

35. estimating tumor growth for the particular patient includes: modeling the tumor growth rate of the particular patient using a pharmacokinetic-pharmacodynamic (PKPD) model having a first term representing the change in tumor size in the particular patient not receiving the drug treatment and a second term representing the contribution to the change in tumor size in the particular patient due to the drug treatment; jointly estimating one or more parameters of the first term and one or more parameters of the second term by fitting the PKPD model to the measured tumor growth data, in part by setting constraints on the one or more parameters of the first term using the population distributions of the one or more patient-specific parameters; A computer system according to any one of claims 24 to 34, comprising:

36. The one or more parameters of the second term are: the concentration of the drug in the plasma of said particular patient; the maximum mortality rate of said particular patient; and Half effective concentration (EC50) 36. The computer system of claim 35, comprising one or more of:

37. 37. The computer system of claim 24, wherein estimating the tumor growth further comprises obtaining an overall response rate for the particular patient receiving the drug treatment.

38. 38. The computer system of claim 24, wherein estimating the tumor growth further comprises obtaining one or more non-target events for the particular patient receiving the drug treatment.

39. 34. The computer system of claim 33, wherein the observations include, for each patient of the plurality of patients, a first observation at the first time indicating that the patient did not have a PFS event before the first time and a second observation at the second time indicating that the patient had a PFS event before the second time.

40. 40. The computer system of any one of claims 24-39, wherein the PFS data corresponds to a particular cancer type, and estimating tumor growth for a particular patient comprises estimating tumor growth for a patient diagnosed with the particular cancer type.

41. 41. The computer system of claim 24, wherein causing the display to present the visual representation of the estimated tumor growth for the particular patient comprises causing the display to display a trajectory of tumor growth for the particular patient if the particular patient had not received the drug treatment.

42. 42. The computer system of any one of claims 24 to 41, wherein the population distribution for the one or more patient-specific parameters comprises a log-normal distribution.

43. 43. The computer system of any one of claims 24 to 42, wherein the PFS data comprises at least one of a digitized PFS plot or a PFS risk table.

44. 44. The computer system of any one of claims 24 to 43, wherein the PFS data indicates the number of patients among the plurality of patients who had a baseline normalized sum longest diameter (SLD) measurement of at least 1.2 or developed new lesions at each of the plurality of observation times and within the most recent time window.

45. 45. The computer system of any one of claims 24 to 44, wherein the plurality of patients represented by the PFS data are patients associated with ineffective drug treatment.

46. 46. ​​The computer system of any one of claims 24 to 45, further comprising adjusting the dose of the drug treatment based on the estimated tumor growth for the particular patient.

47. 1. A non-transitory computer-readable medium comprising instructions for estimating tumor growth, the instructions, when executed by a processor, causing the processor to perform a method comprising: obtaining progression-free survival (PFS) data for a plurality of patients, the PFS data indicating (i) a plurality of observation times and (ii) at each of the plurality of observation times, a number of patients among the plurality of patients who experienced a PFS event within a most recent time window; determining a population distribution of one or more patient-specific parameters based on the PFS data; Obtaining measured tumor growth data for a particular patient receiving drug treatment; (i) estimating tumor growth for the particular patient based on the measured tumor growth data and (ii) the population distribution of the one or more patient-specific parameters; causing a display to present a visual representation of the estimated tumor growth for the particular patient; 1. A non-transitory computer-readable medium comprising:

48. 48. The non-transitory computer-readable medium of claim 47, wherein identifying the population distribution of the one or more patient-specific parameters comprises determining a growth curve function that includes the one or more patient-specific parameters.

49. 49. The non-transitory computer-readable medium of claim 48, wherein the growth curve function comprises at least one of an exponential growth function, a logistic growth function, or an ordinary differential function.

50. 50. The non-transitory computer-readable medium of any one of claims 47 to 49, wherein the one or more patient-specific parameters include a baseline normalized sum of longest diameter (SLD) measurement parameter.

51. 51. The non-transitory computer-readable medium of any one of claims 47 to 50, wherein the one or more patient-specific parameters include a growth rate parameter.

52. 52. The non-transitory computer-readable medium of claim 51, wherein the growth rate parameters comprise baseline growth rate parameters without treatment.

53. 53. The non-transitory computer-readable medium of any one of claims 47-52, wherein the one or more patient-specific parameters comprise a parameter related to a proportion of drug-sensitive tumor cells in a patient of the plurality of patients.

54. 54. The non-transitory computer-readable medium of claim 53, wherein the value of the parameter related to the proportion of drug-sensitive tumor cells in the patient of the plurality of patients ranges from 0 to 1.

55. 49. The non-transitory computer-readable medium of claim 48, wherein the growth curve function is time-dependent.

56. 49. The non-transitory computer-readable medium of claim 48, wherein determining the population distribution of the one or more patient-specific parameters comprises fitting the growth curve function to observations at the multiple observation time points.

57. 50. The non-transitory computer-readable medium of claim 49, wherein the growth curve function is a logistic growth function and the one or more patient-specific parameters include a plurality of parameters of the logistic growth function.

58. estimating tumor growth for the particular patient includes: modeling the tumor growth rate of the particular patient using a pharmacokinetic-pharmacodynamic (PKPD) model having a first term representing the change in tumor size in the particular patient not receiving the drug treatment and a second term representing the contribution to the change in tumor size in the particular patient due to the drug treatment; jointly estimating one or more parameters of the first term and one or more parameters of the second term by fitting the PKPD model to the measured tumor growth data, in part by setting constraints on the one or more parameters of the first term using the population distributions of the one or more patient-specific parameters; 58. The non-transitory computer-readable medium of any one of claims 47 to 57, comprising:

59. The one or more parameters of the second term are: the concentration of the drug in the plasma of said particular patient; the maximum mortality rate of said particular patient; and Half effective concentration (EC50) 59. The non-transitory computer-readable medium of claim 58, comprising one or more of:

60. 60. The non-transitory computer-readable medium of any one of claims 47-59, wherein estimating the tumor growth further comprises obtaining an overall response rate for the particular patient receiving the drug treatment.

61. 61. The non-transitory computer-readable medium of any one of claims 47-60, wherein estimating the tumor growth further comprises obtaining one or more non-target events for the particular patient receiving the drug treatment.

62. 57. The non-transitory computer-readable medium of claim 56, wherein the observations include, for each patient of the plurality of patients, a first observation at the first time indicating that the patient did not have a PFS event before the first time and a second observation at the second time indicating that the patient had a PFS event before the second time.

63. 63. The non-transitory computer-readable medium of any one of claims 47-62, wherein the PFS data corresponds to a particular cancer type, and wherein estimating tumor growth for a particular patient comprises estimating tumor growth for a patient diagnosed with the particular cancer type.

64. 64. The non-transitory computer-readable medium of any one of claims 47-63, wherein causing the display to present the visual representation of the estimated tumor growth for the particular patient comprises causing the display to display a trajectory of tumor growth for the particular patient if the particular patient had not received the drug treatment.

65. 65. The non-transitory computer-readable medium of any one of claims 47 to 64, wherein the population distribution for the one or more patient-specific parameters comprises a log-normal distribution.

66. 66. The non-transitory computer-readable medium of any one of claims 47 to 65, wherein the PFS data comprises at least one of a digitized PFS plot or a PFS risk table.

67. 67. The non-transitory computer-readable medium of any one of claims 47-66, wherein the PFS data indicates the number of patients among the plurality of patients who had a baseline normalized sum longest diameter (SLD) measurement of at least 1.2 or developed a new lesion at each of the plurality of observation times and within the most recent time window.

68. 68. The non-transitory computer-readable medium of any one of claims 47 to 67, wherein the plurality of patients represented by the PFS data are patients associated with ineffective drug treatment.

69. 69. The non-transitory computer readable medium of any one of claims 47-68, further comprising adjusting a dose of the drug treatment based on the estimated tumor growth for the particular patient.

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