Analysis of population PK / PD linked parameters using deep learning

Abstract

A method and system for predicting a set of linked parameters associated with pharmacokinetic and pharmacodynamic effects includes: one or more processors receiving a population dataset including a population pharmacokinetic (PK) dataset and a population pharmacodynamic (PD) dataset; the one or more processors converting the population dataset into a plurality of data density images including a PK data density image and a PD data density image; and the one or more processors predicting the set of linked parameters using the plurality of data density images.

Description

[Technical Field]

[0001] Field This description relates generally to systems and methods for estimating or predicting the pharmacological properties of therapeutic drugs. More specifically, machine learning-based systems and methods are disclosed herein for accurately estimating or predicting the population pharmacokinetic and pharmacodynamic properties of therapeutic drugs. [Background technology]

[0002] background The development of new drugs (e.g., therapeutic drugs) is driven by advances in many fields. Such fields include drug discovery, biotechnology, and in vivo and in vitro pharmacological / toxicological characterization techniques. Before a new therapeutic drug can progress from a molecule or protein in the laboratory to a novel product in a hospital / clinic or local pharmacy, various questions must be answered regarding the efficacy, administration, safety, and side effects associated with the therapeutic drug. Answering these types of questions typically involves a series of carefully designed clinical trials that study various aspects of the new drug candidate.

[0003] Pharmacokinetics (PK) and pharmacodynamics (PD) are scientific fields related to therapeutic development that typically involve mathematical modeling. In general terms, PK (or pK) is often described as "what the body does to the drug," while PD (or pD) is often described as "what the drug does to the body." More specifically, PK can focus on modeling how the body acts on a drug once it is administered and subjected to four bodily processes: absorption, distribution, metabolism, and excretion (ADME). This can be achieved by modeling body concentrations in various regions of the body generally or as a function of time. PD aims to link these modeled drug concentrations to specific drug effects via PD models specifically designed to evaluate those effects. Thus, PK / PD modeling can link systemic drug concentration kinetics to resulting drug effects over time. Such modeling allows for the description and prediction of the time course of various physiological effects (e.g., tumor cell counts, platelet counts, neutrophil counts, etc.) in response to various dosing regimens.

[0004] Traditional mathematical modeling methodologies for PK / PD evaluation can require repeated model evaluation and refinement, with human judgment involved at various steps in the loop. This can be time- and labor-intensive. Examples of such existing mathematical algorithms include expectation maximization, genetic algorithms, and scatter search. These techniques may be optimization-based, which in practice can mean that the modeling scientist performs many function and gradient evaluations, involving significant trial and error. Therefore, effectively using these existing mathematical techniques to model PK and PD requires a significant amount of know-how and computational time. The know-how prerequisites and computational resource requirements represent significant obstacles along the path toward widespread adoption of PK, PD, and PK / PD modeling for non-expert users. Summary of the Invention

[0005] overview In one or more embodiments, a method is provided for predicting a set of linked parameters associated with pharmacokinetic and pharmacodynamic effects. One or more processors receive a population dataset including a population pharmacokinetic (PK) dataset and a population pharmacodynamic (PD) dataset. The one or more processors convert the population dataset into a plurality of data density images including a PK data density image and a PD data density image. The one or more processors predict the set of linked parameters using the plurality of data density images.

[0006] In one or more embodiments, a system for predicting a set of linked parameters associated with pharmacokinetic and pharmacodynamic effects is provided. The system includes a data storage, a computing device communicatively connected to the data storage, and a display system communicatively connected to the computing device. The data storage is configured to store a population dataset including a population pharmacokinetic (PK) dataset and a population pharmacodynamic (PD) dataset. The computing device includes a data manager and a prediction system. The data manager is configured to receive the population dataset and convert the population dataset into a plurality of data density images including a PK data density image and a PD data density image. The prediction system is configured to predict the set of linked parameters using the plurality of data density images. The display system is configured to display a report including a predicted value for each linked parameter in the set of linked parameters.

[0007] In one or more embodiments, a method is provided for predicting a set of linked parameters associated with pharmacokinetic and pharmacodynamic effects. One or more processors receive a population dataset including a population pharmacokinetic (PK) dataset and a population pharmacodynamic (PD) dataset. The one or more processors convert the population dataset into a plurality of binned intensity images including a PK binned intensity image and a PD binned intensity image. The one or more processors predict the set of linked parameters using the plurality of binned intensity images and a deep learning system comprising at least one neural network. [Brief explanation of the drawings]

[0008] For a more complete understanding of the principles disclosed herein and their advantages, reference is now made to the following descriptions taken in conjunction with the accompanying drawings.

[0009] [Figure 1] FIG. 1 is a block diagram of a pharmacokinetic (PK) / pharmacodynamic (PD) evaluation system according to one or more exemplary embodiments.

[0010] [Figure 2] FIG. 1 is a schematic diagram of a prediction workflow according to various embodiments.

[0011] [Figure 3] FIG. 3 is a schematic diagram of an example configuration of the deep learning system of FIG. 2 according to various embodiments.

[0012] [Figure 4] 1 is a flowchart of a method for predicting a set of linked parameters based on a population (PK / PD) dataset, according to various embodiments.

[0013] [Figure 5] 1 is a flowchart of a method for predicting a set of concatenated parameters based on a population PK / PD dataset, according to various embodiments.

[0014] [Figure 6] 1 is a flowchart of a method for training a deep learning system to predict a set of concatenated parameters based on a population PK / PD dataset, according to various embodiments.

[0015] [Figure 7] FIG. 1 is a schematic diagram illustrating a simulation of a population dataset in accordance with various embodiments.

[0016] [Figure 8] FIG. 1 illustrates an exemplary training workflow in accordance with various embodiments.

[0017] [Figure 9] 10A-10C are a series of plots of various forms of compartment modeling according to various embodiments.

[0018] [Figure 10] FIG. 10 is a plot demonstrating the accuracy of estimating linking parameters related to PK and PD effects using the above-described methodology according to various embodiments.

[0019] [Figure 11] FIG. 1 is a block diagram illustrating a computer system according to various embodiments.

[0020] It should be understood that the drawings are not necessarily drawn to scale, and that objects within the drawings are not necessarily drawn to scale relative to each other. The drawings are representations intended to bring clarity and understanding to various embodiments of the devices, systems, and methods disclosed herein. Wherever possible, the same reference numbers will be used throughout the drawings to refer to the same or like parts. Furthermore, it should be understood that the drawings are not intended to limit the scope of the present teachings in any way. DETAILED DESCRIPTION OF THE INVENTION

[0021] Detailed Description I. Overview The principles of pharmacokinetics / pharmacodynamics (PK / PD) have become a well-established quantitative framework for understanding the dose-concentration-effect relationships of various therapeutics (or drugs) and selecting appropriate protocols (e.g., dosages, schedules, etc.) for such therapeutics. As used herein, PK / PD can refer to PK, PD, or both. Population PK / PD modeling refers to the study of pharmacokinetics, pharmacodynamics, or both for a subject (or patient) population. Understanding population PK / PD can include understanding the association between subject (or patient) characteristics and PK / PD differences that can then be used for therapeutic development. For example, population PK / PD can be used to customize drug therapy. Because multiple samples from the same subject are generally not required when analyzing PK / PD for a population, such population-based analyses can be useful for evaluating subject groups that tend to be more difficult to study, such as, but not limited to, subject groups that include subjects with wide geographic distribution.

[0022] Currently available methodologies for analyzing PK / PD, and particularly population PK / PD, can be computationally intensive, time-consuming, and / or require a certain level of knowledge and / or experience. For example, some currently available methodologies use modeling methodologies that may require multiple iterations of model evaluation and refinement, and involve human intervention at various steps within the overall process. The time, computational power, and technical knowledge and / or expertise involved in such modeling methodologies can present obstacles to adopting these modeling methodologies for real-time applications, use by non-technical users, or both.

[0023] Accordingly, this specification describes various exemplary embodiments of machine learning- or deep learning-based systems and methods for rapidly, efficiently, and accurately analyzing population PK / PD with reduced (or, in various cases, no) human intervention. The embodiments described herein enable estimation or prediction of population pharmacokinetics and / or therapeutic drug properties. However, while the systems and methods disclosed herein specifically refer to their application in pharmacokinetics and pharmacodynamics, it should be understood that they are equally applicable to other similar fields, such as toxicokinetics and toxicodynamics.

[0024] The embodiments described herein provide methods and systems for converting a population dataset into a data density image that can then be processed to predict one or more linked parameters relating PK and PD effects. The population dataset can include, for example, at least one population PK dataset (e.g., a clinical population PK dataset) and at least one population PD dataset (e.g., a clinical population PD dataset). The population PK dataset provides data on PK effects observed in a population, while the population PD dataset provides data on PD effects observed in a population. As mentioned above, the PK effect can refer to a dose effect or a body effect on a drug (e.g., drug concentration) in the body. The PD effect can refer to a drug effect (or the effect of a drug on the body) and can depend on the dose effect.

[0025] The data density images can include, for example, but are not limited to, at least one PK data density image and at least one PD data density image. The data density images provide an indication of the number of times or instances (i.e., density) that a particular data point (e.g., a PK value such as a drug concentration or a PD value such as a neutrophil count) occurs within a population dataset. One or more PK data density images and one or more PD data density images are used to predict one or more linkage parameters. These one or more linkage parameters describe the relationship between PK effect and PD effect. Examples of linkage parameters include, but are not limited to, slope, maximum drug effect (E max ), and half-maximal effective concentration (EC 50 ) 。 The slope indicates the drug effect (e.g., drug concentration) relative to the dose effect. Maximum drug effect E max is the maximum effect of a drug at high drug concentrations. 50 is the drug concentration that provides 50% of the drug's maximal or half-maximal effect. The ligation parameter is sometimes called the PD parameter.

[0026] In various embodiments, one or more methods and systems are provided for predicting one or more linkage parameters. A population dataset can be received, including a population PK dataset and a population PD dataset. The population dataset can include data obtained for multiple subjects over different time points and can often be pooled from multiple studies or clinical trials. The population dataset can be converted into multiple data density images. The data density images can include, for example, a PK data density image and a PD data density image. The data density images are processed to predict the value of at least one linkage parameter. In some embodiments, this prediction is performed via a deep learning system. The deep learning system can include, for example, one or more neural network models used to predict the one or more linkage parameters. A linkage parameter is a parameter that links or otherwise relates data from both the population PK dataset and the population PD dataset. In one or more embodiments, the data density image is used to determine a slope defining a PD effect relative to a PK effect (e.g., drug concentration). In other embodiments, alternatively or additionally, one or more other types of linkage parameters may be predicted.

[0027] Understanding the relationship between PD and PK effects in a population can be extremely beneficial for the development of a therapeutic agent, customizing that therapeutic agent to a particular individual, developing clinical trials of a therapeutic agent, developing modified or newer versions of a therapeutic agent, development efforts based on some other type of therapeutic agent, or a combination thereof.

[0028] II. Predicting connectivity parameters using deep learning 1 is a block diagram of a pharmacokinetic (PK) / pharmacodynamic (PD) evaluation system 100 according to one or more exemplary embodiments. The PK / PD evaluation system 100 can be used to evaluate PK and PD effects resulting from administration of a drug (e.g., a therapeutic drug) in a population. In various embodiments, the PK / PD evaluation system 100 is trained based on observed data and then used to predict one or more PK parameters, one or more coupling parameters, or a combination thereof.

[0029] The PK / PD evaluation system 100 can be used in a variety of environments, including, but not limited to, a research environment, a clinical trial environment, a drug development environment, a hospital environment, or any other type of environment. The PK / PD evaluation system 100 can receive and process input data 101 and generate a report 102 that describes and / or contains information based on the input data 101.

[0030] The PK / PD evaluation system 100 includes a computing platform 103, data storage 104, and a display system 106. The computing platform 103 can take a variety of forms. In one or more embodiments, the computing platform 103 includes a single computer (or computer system) or multiple computers in communication with each other. In other examples, the computing platform 103 takes the form of a cloud computing platform. In some embodiments, the computing platform 103 is referred to as a computing device / analysis server. In some embodiments, the computing platform 103 can be a workstation, a mainframe computer, a distributed computing node (part of a "cloud computing" or distributed networking system), a personal computer, a mobile device, etc.

[0031] Data storage 104 and display system 106 each communicate with computing platform 103. Data storage 104 can be communicatively connected to computing platform 103 in a variety of ways, such as, but not limited to, a network connection, which can be either a "hardwired" physical network connection (e.g., Internet, LAN, WAN, VPN, etc.) or a wireless network connection (e.g., Wi-Fi, WLAN, etc.).

[0032] In some examples, data storage 104, display system 106, or both may be considered part of or otherwise integrated with computing platform 103. Thus, in some examples, computing platform 103, data storage 104, and display system 106 may be separate components that communicate with each other, while in other examples, some combination of these components may be integrated together.

[0033] The PK / PD evaluation system 100 includes a data manager 108 and a prediction system 110 implemented on a computing platform 103. Each of the data manager 108 and the prediction system 110 is implemented using hardware, software, firmware, or a combination thereof. The data manager 108 may include, for example, a training data simulation engine, an image rendering engine, or both. The prediction system 110 may also be referred to as a linked parameter prediction engine (or a population linked parameter prediction engine or a PK / PD linked parameter prediction engine).

[0034] It should be understood that the various components or engines of the PK / PD evaluation system 100 can be combined or collapsed into a single engine, component, or module depending on the requirements of a particular application or system architecture. Additionally, in various embodiments, the data storage 104, the data manager 108, the prediction system 110, or a combination thereof, can include additional engines or components as required by a particular application or system architecture.

[0035] In various embodiments, the data manager 108 receives or acquires input data 101. The input data 101 may be obtained from the data storage 104, received from some other source, or a combination thereof. The input data 101 may be generated via one or more samples from one or more subjects. For example, the sample analyzer 112 can be communicatively connected to the data storage 104 via one or more communication links (e.g., via a serial bus, a wireless network connection, etc.). The sample analyzer 112 can be configured to analyze blood samples from a population 114, sometimes referred to as a test population, including multiple subjects. Various time series datasets can be generated from these samples and stored in the data storage 104 for subsequent processing. For example, the sample analyzer 112 can generate a population dataset 116 of the population 114, which is stored in the data storage 104 for processing. The population dataset 116 can include, for example, without limitation, a population PK dataset 118 and a population PD dataset 120. The population PK dataset 118 can include, for example, data points where each data point identifies a dose effect (e.g., drug concentration) in the subjects at a time point (e.g., a particular day, hour, or other unit of time after administration of the drug) for various subjects in the population 114. The population PD dataset 120 can include, for example, data points where each data point identifies a drug effect (e.g., neutrophil count, etc.) in the subjects at a time point (e.g., a particular day, hour, or other unit of time after administration of the drug) for various subjects in the population 114.

[0036] The data manager 108 converts the input data 101 into data density images 134. The data density images 134 include at least one PK data density image and at least one PD data density image. When data density images 134 are generated for the training data 122, they are sometimes referred to as simulated data density images. The data density images are images or representations that provide information about the density of data points in the input data 101 that correspond to selected dose effects and selected time points.

[0037] For example, the data intensity image can take the form of a binned intensity image, in which each pixel value in at least a portion of the binned intensity image indicates the density of data points corresponding to a selected effect (e.g., for a PK-dose effect, for a PD-drug effect) and a selected time point. In some embodiments, in the binned intensity image, data values ​​can be arranged into "bins" with respect to the effect (e.g., for a PK-dose effect, for a PD-drug effect), the time point, or both. For example, time points having values ​​with a selected interval can be replaced by a value representing that interval (e.g., a median value). This may be repeated at multiple intervals across a range forming a series of bins. Effect values ​​(e.g., drug concentration values, neutrophil counts, etc.) having values ​​with a selected interval can be replaced by a value representing that interval (e.g., a median value). This may be repeated at multiple intervals across a range forming a series of bins. In other embodiments, the data density image 134 can take the form of some other type of quantized representation of the input data 101.

[0038] The data manager 108 sends the data density image 134 to the prediction system 110 for processing. The prediction system 110 is a machine learning or deep learning system. In one or more embodiments, the prediction system 110 includes a neural network system 111. The neural network system 111 includes one or more neural network models. For example, the neural network system 111 may include a training module 126 and a prediction module 128. When the neural network system 111 is being trained, the training module 126 may process the data density image 134 generated based on the training data 122. Once trained, the neural network system 111 may be used to predict a set of connectivity parameters 130, a set of PK parameters 132, or both, based on the data density image 134 generated based on the population dataset 116. Thus, the type of data density image 134 provided to the neural network system 111 may take different forms depending on whether the neural network system 111 is in training mode or prediction mode.

[0039] The set of linkage parameters 130 may include, for example, slope, half-maximal effective concentration (EC 50 ), or maximum effect (E max ) The slope can indicate the drug effect (e.g., drug concentration) relative to the dose effect. As an example, the slope associated with the drug effect on proliferating progenitor cells can describe how increasing drug concentration inhibits the synthesis of proliferating progenitor cells. The maximum drug effect E max is the maximum effect of a drug at high drug concentrations. 50is the drug concentration that provides 50% of the drug's maximal or half-maximal effect. With respect to population 114, the linkage parameters of the set of linkage parameters 130 can be the arithmetic mean (or average), median, standard deviation, or other population-based descriptive statistical metric of the parameters. For example, the slope can be the mean slope, median slope, or some other slope value that represents the slope value associated with population 114. In some embodiments, the set of linkage parameters 130 may also be referred to as a set of PD parameters.

[0040] The set of PK parameters 132 may include, for example, area under the curve (AUC), minimum concentration (C min ), maximum concentration (C max ), C max Time to reach (T max ), elimination half-life (t 1 / 2 ), mean residence time (MRT), last measurable concentration (C Last ) (e.g., before the next dose), C Last Time to reach (T Last ), or another PK parameter. With respect to population 114, the PK parameters of set of PK parameters 132 can be the arithmetic mean (or average), median, standard deviation, or another population-based descriptive statistical metric of the parameters. For example, the AUC can be the mean AUC, median AUC, or some other AUC value representing the AUC corresponding to the population PK dataset 118 for population 114. As another example, C min is the average C min , median C min , or C related to the population PK dataset 118 min some other C value min It can be a value.

[0041] After these one or more parameters are predicted, the prediction system 110 can generate a report 102 that can be displayed on the display system 106. The display system 106 in some embodiments may be implemented in a client terminal 136 communicatively connected to the computing platform 103. In various embodiments, the client terminal 136 can be a thin-client computing device. In various embodiments, the client terminal 136 can be a personal computing device having a web browser (e.g., Internet Explorer™, Firebox™, Safari™, etc.) that can be used to control the operation of the data storage 104, the data manager 108, the prediction system 110, or a combination thereof.

[0042] The report 102 may include, for example, values ​​for a set of concatenated parameters 130, a set of PK parameters 132, or both. In one or more examples, the report 102 may include one or more recommended actions based on the predicted PK time course.

[0043] 2 is a schematic diagram of a prediction workflow according to various embodiments. Prediction workflow 200 is an example of how prediction of a set of linked parameters can be implemented using PK / PD evaluation system 100 of FIG. 1. Prediction workflow 200 includes converting a population PK dataset 202 and a population PD dataset 204 into a PK data density image 206 and a PD data density image 208, respectively. Population PK dataset 202 and population PD dataset 204 are examples of implementations of population PK dataset 118 and population PD dataset 120 of FIG. 1. PK data density image 206 and PD data density image 208 are examples of implementations of data density image 134 of FIG. 1.

[0044] Both the PK data density image 206 and the PD data density image 208 can be input to a deep learning system 210, which is an example of an implementation of the prediction system 110 of FIG. 1. The deep learning system 210 processes the PK data density image 206 and the PD data density image 208 to predict a set of linked parameters 212. The set of linked parameters 212 includes gradients, maximum drug effect (E), and the like. max ), half-maximal effective concentration (EC 50 ), or another linking parameter that describes the relationship between the population PK dataset 202 and the population PD dataset 204.

[0045] 3 is a schematic diagram of an example configuration of deep learning system 210 of FIG. 2 in accordance with various embodiments. In one or more embodiments, deep learning system 210 includes at least four neural networks: neural network 302, neural network 304, neural network 306, and neural network 308. In other embodiments, deep learning system 210 may include some other number or configuration of neural networks. In one or more embodiments, one or more of neural network 302, neural network 304, neural network 306, and neural network 308 are convolutional neural networks.

[0046] Neural network 302 can receive PK data density image 206 for processing. Neural network 304 can receive PD data density image 208 for processing. In one or more embodiments, PK data density image 206 and PD data density image 208 are binned intensity images. For example, PK data density image 206 can be a binned intensity image in which a pixel or group of pixels for a particular drug concentration (concentration interval or range or "bin") and a particular time point (or time interval or "bin") has an intensity that represents the density (e.g., number of instances) of that particular drug concentration (concentration interval or range or "bin") and particular time point (or time interval or "bin"). For example, the higher the intensity of a given pixel or group of pixels, the greater the number of instances (e.g., number of subjects) in which the same drug concentration (or drug concentration within the same interval or bin) was measured for the same time point (or same period, time interval, or time bin).

[0047] Neural network 302 processes PK data density image 206 to generate PK model output 310. Neural network 304 processes PD data density image 208 to generate PD model output 312. In one or more embodiments, PK model output 310 and PD model output 312 are model parameters of neural network 302 and neural network 304, respectively. In other embodiments, PK model output 310 and PD model output 312 are some other type of output corresponding to PK data density image 206 and PD data density image 208, respectively. In one or more embodiments, PK model output 310 and PD model output 312 are in the form of vectors.

[0048] The PK model output 310 can be sent as input to a neural network 306. In one or more embodiments, the neural network 306 is a fully connected neural network. The neural network 306 processes the PK model output 310 and generates a set of PK parameters 314 as output. The set of PK parameters 314 can include, for example, area under the curve (AUC), minimum concentration (C min ) or maximum concentration (C max ) may include at least one of:

[0049] In one or more embodiments, both the PK model output 310 and the PD model output 312 are sent to a merging unit 316 to form a merged input 318 that is sent to the neural network 308. The merging unit 316 can be implemented using, for example, a catenation network or unit. In some embodiments, the PK model output 310 and the PD model output 312 are sent directly as inputs to the neural network 308 and are merged, concatenated, or linked in some way within the neural network 308. In one or more embodiments, the neural network 308 is a multi-layer perceptual network.

[0050] The neural network 308 processes its inputs (e.g., the merged input 318 or both the PK model output 310 and the PD model output 312) to generate a set of linked parameters 212 as described above in Figure 2. In some embodiments, the set of PK parameters 314 and the set of linked parameters 212 are merged to form a final output vector that includes values ​​of the various PK and linked parameters predicted by the deep learning system 210.

[0051] III. Exemplary Methods for Predicting a Set of Linkage Parameters 4 is a flowchart of a method for predicting a set of joint parameters based on a population (PK / PD) dataset, according to various embodiments. In some embodiments, the method 400 can be implemented by the PK / PD evaluation system 100 described in FIG.

[0052] Step 402 includes receiving, by one or more processors, population datasets including a population pharmacokinetic (PK) dataset and a population pharmacodynamic (PD) dataset. The population PK dataset can include, for example, dose-effect (e.g., drug concentration) time series data. The population PD dataset can include, for example, drug-effect (e.g., neutrophil count) time series data.

[0053] Step 404 includes converting, by one or more processors, the population dataset into a plurality of data density images, including a PK data density image and a PD data density image. In one or more embodiments, the PK data density image and the PD data density image are binned intensity images. In one or more embodiments, the PK data density image is a binned intensity image, where each pixel value in at least a portion of the binned intensity image indicates the density of data points corresponding to a selected dose effect and a selected time point. In one or more embodiments, the PD data density image is a binned intensity image, where each pixel value in at least a portion of the binned intensity image indicates the density of data points corresponding to a selected dose effect and a selected time point.

[0054] Step 406 includes predicting, by one or more processors, a set of linking parameters using the plurality of data density images. The linking parameters in the set of linking parameters provide a correspondence or otherwise link between the population PK dataset and the population PD dataset. In one or more embodiments, the set of linking parameters includes slope, half-maximal effective concentration (EC 50 ), or maximum effect (E max ) may include at least one of:

[0055] 5 is a flowchart of a method for predicting a set of joint parameters based on a population PK / PD dataset, according to various embodiments. In some embodiments, the method 500 can be implemented by the PK / PD evaluation system 100 described in FIG.

[0056] Step 502 includes training a deep learning system by one or more processors using simulated population datasets, including a simulated pharmacokinetic (PK) dataset and a simulated pharmacodynamic (PD) dataset. The simulated PK dataset and the simulated PD dataset can be population-level datasets generated in a variety of ways and using any number or combination of models.

[0057] Step 504 includes receiving, by one or more processors, a population dataset including a population pharmacokinetic (PK) dataset and a population pharmacodynamic (PD) dataset. In some embodiments, the population dataset may be a real-world dataset or a clinical dataset.

[0058] Step 506 includes converting, by one or more processors, the population dataset into a plurality of binned intensity images, including a PK binned intensity image and a PD binned intensity image, each of which includes pixels where the value of a given pixel indicates the density of data points in the dataset from which the binned intensity image was generated for a selected effect (e.g., for a PK-dose effect, for a PD-drug effect) at a selected time point.

[0059] Step 508 includes predicting, by one or more processors, a set of linkage parameters using the plurality of binned intensity images and a deep learning system. The set of linkage parameters includes gradient, half-maximal effective concentration (EC 50 ), or maximum effect (E max ) may include at least one of:

[0060] IV. Training the Deep Learning System with Simulated Population PK and PD Data 6 is a flowchart of a method 600 for training a deep learning system to predict a set of concatenated parameters based on a population PK / PD dataset, according to various embodiments. Method 600 is an example of how step 502 of FIG. 5 can be performed. Furthermore, method 600 can be implemented by the PK / PD evaluation system 100 described in FIG. 1.

[0061] Step 602 includes receiving simulated population training data sets including a simulated pharmacokinetic (PK) data set and a simulated pharmacodynamic (PD) data set. The simulated PK data set and the simulated PD data set can be population-level data sets generated in a variety of ways and using any number or combination of models.

[0062] Step 604 includes converting the simulated population dataset into a plurality of simulated data density images, including a simulated PK data density image and a simulated PD data density image, which may include, for example, a binned intensity image.

[0063] Step 606 includes training a deep learning system to predict a set of parameters, including at least the set of connected parameters, based on a plurality of simulated data density images. Step 606 can be performed in various ways. In one or more embodiments, step 606 can include initializing a self-organizing neural network of the deep learning system to enable training.

[0064] 7 is a schematic diagram illustrating a simulation of a population dataset according to various embodiments. A simulated PK model 700 and a simulated PD model 702 can be used to generate a simulated PK dataset 704 and a simulated PD dataset 706, respectively. The simulated PK model 700 and the simulated PD model 702 can generate these simulated datasets based on effects associated with one or more therapeutic agents (drugs).

[0065] The simulated PK dataset 704 may also be referred to as a simulated population PK dataset, and the simulated PD dataset 706 may also be referred to as a simulated population PD dataset. For example, the simulated PK dataset 704 may simulate drug concentrations over time (e.g., for discrete time points). The simulated PD dataset 706 may simulate drug effects (e.g., neutrophil count or some other effect) over time (e.g., for discrete time points). The simulated PK dataset 704 and the simulated PD dataset 706 are generated as time-series datasets based on sampling time 708 and sampling time 710, respectively. In one or more embodiments, the sampling time 708 and sampling time 710 are the same or are matched.

[0066] Each of the simulated PK model 700 and the simulated PD model 702 can be customized with model parameters such that the corresponding simulation model generates one or more discrete time series (or time series data sets). Each discrete time series can represent data (e.g., PK or PD) for one simulated administration of a therapeutic agent to a simulated test subject. In one or more embodiments, the simulated PK data set 704 and the simulated PD data set 706 each include multiple time series for a simulated population. In some embodiments, the simulated PK model 700, the simulated PD model 702, or both, augment the simulated data with real or clinical data points to form the simulated PK data set 704, the simulated PD data set 706, or both, respectively.

[0067] The simulated PD model 702 can be implemented in a variety of ways. In one or more embodiments, the simulated PD model 702 can be implemented using at least one of a one-compartment model, a two-compartment model, a Michaelis-Menten two-compartment model, or another type of model.

[0068] For the PK1 compartment model, the model parameters of the simulated PK model 700 can be customized to include, but are not limited to, the volume of distribution of the central compartment, the rate of absorption into the central compartment, the rate of elimination from the central compartment, one or more other types of parameters, or a combination thereof. For the PK2 compartment model, the model parameters of the simulated PK model 700 can be customized to include, but are not limited to, the volume of distribution of the central compartment, the volume of distribution of the peripheral compartments, the rate of absorption into the central compartment, the rate of elimination from the central compartment, the intercompartmental clearance between the central and peripheral compartments, one or more other types of model parameters, or a combination thereof.

[0069] In the case of a Michaelis-Menten PK two-compartment model, the model parameters of the simulation PK model 700 can be customized to include, but are not limited to, the volume of distribution of the central compartment, the volume of distribution of the peripheral compartment, the rate of absorption into the central compartment, the rate of elimination from the central compartment, the intercompartmental clearance between the central and peripheral compartments, the Michaelis-Menten constant associated with the nonlinear clearance mechanism, one or more other types of model parameters, or a combination thereof.

[0070] The simulated PD model 702 can be implemented in a variety of ways. For example, the simulated PD model 702 may be implemented using an indirect response model (i.e., an inhibitory k in , inhibition k out , stimulus k in , stimulus k out , or a combination thereof), a biota model, a signal transduction model, or some other type of simulation model.

[0071] The simulated PK dataset 704 and the simulated PD dataset 706 can be converted into simulated data density images (e.g., binned intensity images) in a manner similar to the conversion of the population PK dataset 202 and the population PD dataset 204 into the PK data density image 206 and the PD data density image 208, respectively, in Figure 2. The deep learning system 210 described in Figure 2 can be trained using these simulated data density images.

[0072] 8 is a diagram of an exemplary training workflow 800 according to various embodiments. The training workflow 800 is a high-level diagram of how simulated PK data can be generated and used to create a training data set.

[0073] As shown herein, simulated time-series concentration data 802 are generated using one or more PK compartment models, which involves first setting (via inputs) simulation parameters for one or more PK compartment models and then running a simulation of the PK compartment models to generate simulated time-series concentration data 802 for one or more existing or potential future therapeutic agents.

[0074] Examples of simulation parameters for PK compartmental models include, but are not limited to, the following: administration scheme (e.g., subcutaneous, oral, intravenous, etc.), molecular class (e.g., small or large molecule), molecular species (e.g., drugs, mAbs, proteins, enzymes, etc.), compartmental model specific parameters (e.g., central compartment volume of distribution, absorption constant, desorption constant, etc.), modeled species (e.g., mammal, rodent, human, non-human primate, etc.), modeled species demographics (e.g., age, weight, sex, etc.), baseline albumin, baseline tumor size, etc.

[0075] In various embodiments, a one-compartment model can be used to simulate the time-series concentration data 802. For a PK1 compartment model, compartment parameters that can be set include, but are not limited to, the volume of distribution of the central compartment, the rate of absorption into the central compartment, the rate of elimination from the central compartment, etc.

[0076] In various embodiments, a two-compartment model can be used to simulate the time-series concentration data 802. For the PK2-compartment model, compartment parameters that can be set include, but are not limited to, the volume of distribution of the central compartment, the volume of distribution of the peripheral compartment, the rate of absorption into the central compartment, the rate of elimination from the central compartment, the intercompartmental clearance between the central compartment and the peripheral compartment, etc.

[0077] In various embodiments, a Michaelis-Menten PK two-compartment model can be used to simulate the time series concentration data 802. For the Michaelis-Menten PK two-compartment model, compartment parameters that can be set include, but are not limited to, the following: volume of distribution of the central compartment, volume of distribution of the peripheral compartment, rate of absorption into the central compartment, rate of elimination from the central compartment, intercompartmental clearance between the central and peripheral compartments, Michaelis-Menten constants associated with nonlinear clearance mechanisms, etc.

[0078] After the simulated time series concentration data 802 is generated, it is sparsely sampled 806 to form a subset of simulated time series concentration training datasets 808, each of which is further processed using non-compartmental analysis (NCA) 804 to calculate their corresponding simulated PK parameter values ​​810. Examples of types of simulated PK parameter values ​​include, but are not limited to: AUC, C max , C min , C trough , T max , MRT, T Last , or t 1 / 2 .

[0079] 9 is a series of plots 900 for various forms of compartmental modeling according to various embodiments. The series of plots 900 illustrates how compartmental modeling can be used to simulate time series concentration data combined with PK parameters predicted using NCA to form a training data set, according to various embodiments.

[0080] In the example shown in Figure 9, three different compartmental models (i.e., 1-compartment 910, 2-compartment 912, and 2-compartment Michaelis-Menten 914) were used to generate a simulated time series concentration dataset 902. To demonstrate the effect of administration scheme on the simulated time series concentration dataset 902, the same compartmental model simulation was run using different treatment administration scheme settings (i.e., bolus 906 and oral / subcutaneous 908).

[0081] As described above, after the simulated time series concentration datasets 902 are generated, they are further processed using NCA to calculate their corresponding simulated PK parameter values ​​904. In various embodiments, the simulated time series concentration datasets are of one or more existing or potential future therapeutic agents.

[0082] V. Experimental Results The improved systems and methods disclosed herein were compared to conventional approaches for predicting joint population PK / PD parameter values ​​for agents (eg, drugs).

[0083] FIG. 10 is a plot 1000 demonstrating the accuracy of estimating a linkage parameter related to PK and PD effects using the above-described methodology according to various embodiments. As shown in plot 1000, the “true” linkage parameter values ​​(e.g., population PK / PD linkage parameter values) were plotted against the “estimated” or “predicted” linkage parameter values ​​generated by the image-based NN prediction methodology disclosed above for 1000 samples. In plot 1000, the linkage parameter is a slope, which relates drug effect to drug concentration. Plot 1000 shows that the true slope and estimated slope were closely correlated with each other across the entire range of slope values. Thus, the image-based NN prediction methodology described herein can accurately estimate or predict a linkage parameter relating PK and PD across a range of linkage parameter values.

[0084] VI. Computer-Implemented Systems FIG. 11 is a block diagram illustrating a computer system according to various embodiments. Computer system 1100 may be an example of an implementation for computing device 93 of FIG. 1. In various embodiments of the present teachings, computer system 1100 may include a bus 1102 or other communication mechanism for communicating information and a processor 1104 coupled to bus 1102 for processing information. In various embodiments, computer system 1100 may also include memory, which may be random access memory (RAM) 1106 or other dynamic storage device, coupled to bus 1102 for determining instructions to be executed by processor 1104. The memory may also be used for storing temporary variables or other intermediate information during execution of instructions to be executed by processor 1104. In various embodiments, computer system 1100 may further include read-only memory (ROM) 1108 or other static storage device coupled to bus 1102 for storing static information and instructions for processor 1104. A storage device 1110, such as a magnetic disk or optical disk, may be provided and coupled to bus 1102 for storing information and instructions.

[0085] In various embodiments, computer system 1100 can be coupled via bus 1102 to a display 1112, such as a cathode ray tube (CRT) or liquid crystal display (LCD), for displaying information to a computer user. An input device 1114, including alphanumeric and other keys, can be coupled to bus 1102 for communicating information and command selections to processor 1104. Another type of user input device is a cursor control device 1116, such as a mouse, trackball, or cursor direction keys, for communicating directional information and command selections to processor 1104 and controlling cursor movement on display 1112. This input device 1114 typically has two degrees of freedom, a first axis (i.e., x) and a second axis (i.e., y), that allow the device to specify a position in a plane. However, it should be understood that input devices 1114 that allow for three-dimensional (x, y, and z) cursor movement are also contemplated herein.

[0086] Consistent with a particular implementation of the present teachings, results may be provided by computer system 1100 in response to processor 1104 executing one or more sequences of one or more instructions contained in memory 1106. Such instructions may be read into memory 1106 from another computer-readable medium or computer-readable storage medium, such as storage device 1110. Execution of the sequences of instructions contained in memory 1106 may cause processor 1104 to perform the processes described herein. Alternatively, hardwired circuitry may be used in place of or in combination with software instructions to implement the present teachings. Thus, implementation of the present teachings is not limited to any specific combination of hardware circuitry and software.

[0087] The terms "computer-readable medium" (e.g., data store, data storage, etc.) or "computer-readable storage medium," as used herein, refer to any medium that participates in providing instructions to processor 1104 for execution. Such a medium may take many forms, including, but not limited to, non-volatile media, volatile media, and transmission media. Examples of non-volatile media may include, but are not limited to, optical, solid-state, and magnetic disks, such as storage device(s) 1110. Examples of volatile media may include, but are not limited to, dynamic memory, such as memory 1106. Examples of transmission media may include, but are not limited to, coaxial cables, copper wire, and fiber optics, including the wires that comprise bus 1102.

[0088] Common forms of computer-readable media include, for example, floppy disks, flexible disks, hard disks, magnetic tape or any other magnetic medium, CD-ROMs, any other optical medium, punch cards, paper tape, any other physical medium with a pattern of holes, RAM, PROMs, and EPROMs, flash EPROMs, any other memory chip or cartridge, or any other tangible medium from which a computer can read.

[0089] In addition to computer-readable media, instructions or data may be provided as signals on a transmission medium included in a communication device or system to provide sequences of one or more instructions to the processor 1104 of the computer system 1100 for execution. For example, a communication device may include a transceiver having signals indicative of instructions and data. The instructions and data are configured to cause one or more processors to implement the functions outlined in this disclosure. Representative examples of data communication transmission connections include, but are not limited to, a telephone modem connection, a wide area network (WAN), a local area network (LAN), an infrared data connection, an NFC connection, etc.

[0090] It should be understood that the flowcharts, diagrams, and accompanying disclosure described herein can be implemented using computer system 1100 as a standalone device or on a distributed network of shared computer processing resources, such as a cloud computing network.

[0091] The methodologies described herein can be implemented by various means depending on the application. For example, these methods can be implemented in hardware, firmware, software, or any combination thereof. In the case of a hardware implementation, the processing unit can be implemented in one or more application-specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field-programmable gate arrays (FPGAs), processors, controllers, microcontrollers, microprocessors, electronic devices, other electronic units designed to perform the functions described herein, and / or combinations thereof.

[0092] In various embodiments, the methods of the present teachings may be implemented as firmware and / or software programs and applications written in conventional programming languages ​​such as C, C++, Python, etc. When implemented as firmware and / or software, the embodiments described herein can be implemented on a non-transitory computer-readable medium having stored thereon a program for causing a computer to perform the methods described above. It should be understood that the various engines described herein can be provided on a computer system such as computer system 1100, whereby processor 1104 performs the analyses and decisions provided by these engines according to instructions provided by any one or a combination of memory components 1106 / 1108 / 1110 and user input provided via input device 1114.

[0093] VII. Exemplary Embodiments Various exemplary embodiments are described herein.

[0094] In one or more embodiments, a system for predicting a set of linked parameters associated with pharmacokinetic and pharmacodynamic effects is provided. The system includes a data storage, a computing device communicatively connected to the data storage, and a display system communicatively connected to the computing device. The data storage is configured to store a population dataset including a population pharmacokinetic (PK) dataset and a population pharmacodynamic (PD) dataset. The computing device includes a data manager and a prediction system. The data manager is configured to receive the population dataset and convert the population dataset into a plurality of data density images including a PK data density image and a PD data density image. The prediction system is configured to predict the set of linked parameters using the plurality of data density images. The display system is configured to display a report including a predicted value for each linked parameter in the set of linked parameters.

[0095] In one or more embodiments, a non-transitory computer-readable medium storing computer instructions for predicting population linked parameter values ​​includes instructions for receiving a population dataset including a population pharmacokinetic (PK) dataset and a population pharmacodynamic (PD) dataset, converting the population dataset into a plurality of data density images including a PK data density image and a PD data density image, and predicting a set of linked parameters using the plurality of data density images.

[0096] In one or more embodiments, a non-transitory computer-readable medium storing computer instructions for predicting population linkage parameter values ​​includes instructions for receiving a population dataset including a population pharmacokinetic (PK) dataset and a population pharmacodynamic (PD) dataset, converting the population dataset into a plurality of binned intensity images including a PK binned intensity image and a PD binned intensity image, and predicting a set of linkage parameters using the plurality of binned intensity images and a deep learning system comprising at least one neural network.

[0097] In one or more embodiments, a method for training a deep learning system to predict one or more coupling parameters is provided. The method includes receiving a simulated training population including a simulated pharmacokinetic (PK) dataset and a simulated pharmacodynamic (PD) dataset. The simulated PK dataset and the simulated PD dataset can be population-level datasets generated in various ways using any number or combination of models. The method includes converting the simulated population dataset into a plurality of simulated data density images, including a simulated PK data density image and a simulated PD data density image. The method includes training the deep learning system to predict a set of parameters including at least the set of coupling parameters based on the plurality of simulated data density images.

[0098] In one or more embodiments, the PK data density image of one or more exemplary embodiments described herein is a binned intensity image in which each pixel value in at least a portion of the binned intensity image indicates the density of data points corresponding to a selected dose effect and a selected time point.

[0099] In one or more embodiments, the PD data density image of one or more exemplary embodiments described herein is a binned intensity image in which each pixel value in at least a portion of the binned intensity image indicates the density of data points corresponding to a selected dose effect and a selected time point.

[0100] In one or more embodiments, the set of linkage parameters of one or more exemplary embodiments described herein may include slope, half-maximal effective concentration (EC 50 ) or maximum effect (E max ) contains at least one of the following:

[0101] In one or more embodiments, one or more exemplary method embodiments described herein include predicting, by one or more processors, a set of PK parameters using the PK data density image, the set of PK parameters including area under the curve (AUC), minimum concentration (C min ) or maximum concentration (C max ) contains at least one of the following:

[0102] In one or more embodiments, predicting the set of concatenated parameters in one or more of the exemplary method embodiments described herein includes predicting, by one or more processors, the set of concatenated parameters using a plurality of data density images and a deep learning system.

[0103] In one or more embodiments, the deep learning system of one or more example embodiments described herein includes a neural network system.

[0104] In one or more embodiments, the deep learning system of one or more example embodiments described herein includes at least one convolutional neural network.

[0105] In one or more embodiments, one or more example embodiments described herein include training a deep learning system for use in predicting the set of linkage parameters, the training being performed using a simulated PK dataset and a simulated PD dataset.

[0106] In one or more embodiments, the data storage and computing devices of one or more of the exemplary embodiments described herein are part of an integrated apparatus.

[0107] In one or more embodiments, the data storage of one or more exemplary embodiments described herein is hosted by a device different from the computing device of one or more exemplary embodiments described herein.

[0108] In one or more embodiments, the data storage and computing devices of one or more of the exemplary embodiments described herein are part of a distributed network system.

[0109] VIII. Further Considerations The teachings described herein are not limited to the exemplary embodiments and applications or their methods of operation described herein. Furthermore, the division of sections herein is merely for ease of review and does not limit any combination of the elements described. In describing various embodiments, the specification may present a method and / or process as a particular sequence of steps. However, to the extent that the method or process does not rely on the particular order of steps described herein, the method or process should not be limited to the particular order of steps described, and one of ordinary skill in the art can readily understand that the order may be changed and still be within the spirit and scope of various embodiments. Furthermore, when a reference is made to a list of elements (e.g., elements a, b, c), such reference is intended to include any one of the listed elements by itself, any combination of fewer than all of the listed elements, and / or all combinations of the listed elements.

[0110] The figures may show simplified or partial views, and dimensions of elements in the figures may be exaggerated or not to scale. Additionally, when the terms "on," "attached to," "connected to," "coupled to," or similar terms are used herein, an element (e.g., a material, layer, substrate, etc.) can be "on," "attached to," "connected to," or "coupled to" another element, regardless of whether the element is directly on, directly attached to, connected to, or coupled to the other element, or whether there are one or more intervening elements between the one element and the other element.

[0111] Unless otherwise defined, scientific and technical terms used in connection with the present teachings described herein shall have the meanings commonly understood by those of ordinary skill in the art. Furthermore, unless the context otherwise requires, singular terms shall include the plural and plural terms shall include the singular. Generally, the nomenclature and techniques utilized in connection with the chemistry, biochemistry, molecular biology, pharmacology, and toxicology described herein are those well known and commonly used in the art.

[0112] As used herein, "substantially" means sufficient to function for its intended purpose. Thus, the term "substantially" accounts for minor, insignificant variations from an absolute or perfect state, dimension, measurement, result, etc., that would be expected by one of ordinary skill in the art, but that do not significantly affect overall performance. When used in reference to a numerical value, or a parameter or characteristic that can be expressed as a numerical value, "substantially" means within 10 percent.

[0113] The term "plurality" means two or more.

[0114] As used herein, the term "plurality" can be 2, 3, 4, 5, 6, 7, 8, 9, 10 or more.

[0115] As used herein, the phrase "area under the curve" (AUC) can refer to the area under the curve that represents the variation of therapeutic (drug) concentration in the plasma of a subject as a function of time after administration.

[0116] As used herein, "maximum concentration" (C max The phrase "maximum (or peak) serum concentration" can refer to the maximum (or peak) serum concentration that a therapeutic agent (drug) achieves in a particular compartment or test area of ​​the body after the drug is administered and before a second dose is administered.

[0117] As used herein, "minimum concentration" (C min ) or "trough concentration" (C trough The phrase "minimum (or peak) serum concentration" can refer to the minimum (or peak) serum concentration that a therapeutic agent (drug) achieves in a particular compartment or test area of ​​the body after the drug is administered and before a second dose is administered.

[0118] As used herein, "time to maximum concentration" (T max The term ) can refer to the time to reach maximum concentration after a therapeutic (drug) dose is administered before the next dose is administered.

[0119] As used herein, "half-life" (t 1 / 2 The term ) can refer to the time it takes for the concentration of a therapeutic agent (drug) in plasma to reach half of its steady-state value.

[0120] As used herein, the phrase "minimum inhibitory concentration" (MIC) can refer to the lowest concentration of an antibiotic that completely inhibits the growth of a microorganism in vitro.

[0121] As used herein, "maximum effective concentration" (E max The phrase maximal pharmacological effect can refer to the maximum pharmacological effect provided by a therapeutic agent (drug).

[0122] As used herein, "half maximal effective concentration" (EC 50 The phrase "maximum pharmacological effect" can refer to the concentration of a therapeutic agent (drug) at which 50% of the maximum pharmacological effect is achieved.

[0123] As used herein, the phrase "compartment model" or "compartment modeling" can refer to one or more mathematical modeling techniques used to predict PK parameters (indicative of ADME) of synthetic or natural therapeutic agents (drugs) in test subjects by modeling the concentrations of the therapeutic agent in different regions of the body. Within these mathematical models, different regions of the body can be divided into parts called compartments in which the therapeutic agent can be assumed to behave similarly.

[0124] As used herein, the phrase "non-compartmental model" (NCA) can refer to one or more model-independent techniques (meaning that they do not rely on assumptions about body compartments) used to predict PK parameters (indicative of ADME) of therapeutic drugs administered to test subjects. NCA allows for the calculation of PK parameters of therapeutic drugs from measured drug concentration time courses.

[0125] As used herein, "biological" or "macrotherapeutic macromolecule" can refer to proteins and other biological macromolecules that have a therapeutic effect.

[0126] As used herein, "therapeutic compound" or "small molecule therapeutic" can refer to any organic compound that affects biological processes and has a relatively low molecular weight of less than 900 daltons.

[0127] As used herein, "artificial neural network" or "neural network" (NN) can refer to a mathematical algorithm or computational model. A neural network can predict an output for a received input using one or more layers of nonlinear units. Some neural networks include one or more hidden layers in addition to an output layer. The output of each hidden layer is used as the input to the next layer in the network, i.e., the next hidden layer or the output layer. Each layer of the network generates an output from the received input according to the current values ​​of each set of parameters.

[0128] Neural networks can process information in two ways: when they are being trained, they may be in "learning mode," and when they actually use what they have learned, they may be in "inference (or prediction) mode." Neural networks can learn through a feedback process called backpropagation, which allows the network to adjust the weight coefficients of individual nodes in intermediate hidden layers (modify their behavior) so that their outputs match those of the training data. In other words, neural networks can receive training data (training examples) and automatically learn how to arrive at the correct output, even when presented with a new range or set of inputs. Examples of types of neural networks include, but are not limited to, feedforward neural networks (FNNs), recurrent neural networks (RNNs), modular neural networks (MNNs), convolutional neural networks (CNNs), and ResNets (residual neural networks).

[0129] Accordingly, while the present teachings have been described in conjunction with various embodiments, it is not intended that the present teachings be limited to such embodiments. On the contrary, the present teachings encompass various alternatives, modifications, and equivalents, as will be appreciated by those skilled in the art.

Claims

1. 1. A method for predicting a set of linked parameters related to pharmacokinetic and pharmacodynamic effects, comprising: receiving, by one or more processors, population datasets including a population pharmacokinetic (PK) dataset and a population pharmacodynamic (PD) dataset; converting, by the one or more processors, the population dataset into a plurality of data density images, including a PK data density image and a PD data density image, wherein the PK data density image reflects the density of data points corresponding to a selected dose effect and a selected time point, and the PD data density image reflects the density of data points corresponding to a selected drug effect and a selected time point; predicting, by the one or more processors, the set of linkage parameters using the plurality of data density images and a deep learning system, wherein the deep learning system receives the plurality of data density images as input and outputs the set of predicted linkage parameters, the deep learning system being trained using a simulated PK dataset and a simulated PD dataset, wherein the simulated PK dataset is generated based on simulation of drug concentrations with respect to time points, and the simulated PD dataset is generated based on simulation of drug effects with respect to time points.

2. 10. The method of claim 1, wherein the PK data density image is a binned intensity image, and each pixel value in at least a portion of the binned intensity image indicates the density of a data point corresponding to a selected dose effect and a selected time point.

3. 2. The method of claim 1, wherein the PD data density image is a binned intensity image, and each pixel value in at least a portion of the binned intensity image indicates the density of a data point corresponding to a selected dose effect and a selected time point.

4. The set of linkage parameters includes slope, half-maximal effective concentration (EC 50 ), or maximum effect (E max 10. The method of claim 1, comprising at least one of:

5. predicting, by the one or more processors, a set of PK parameters using the PK data density image, wherein the set of PK parameters includes area under the curve (AUC), minimum concentration (C min ), or maximum concentration (C max 10. The method of claim 1, further comprising predicting a set of PK parameters comprising at least one of:

6. The method of claim 1 , wherein the deep learning system comprises a neural network system.

7. The method of claim 1 , wherein the deep learning system includes at least one convolutional neural network.

8. The method of claim 1, further comprising using the simulated PK dataset and the simulated PD dataset to train the deep learning system used to predict the set of linked parameters.

9. 1. A system for predicting a set of linked parameters related to pharmacokinetic and pharmacodynamic effects, comprising: a data store for storing population datasets, including a population pharmacokinetic (PK) dataset and a population pharmacodynamic (PD) dataset; a computing device communicatively connected to the data store, a data manager configured to receive the population dataset and convert the population dataset into a plurality of data density images, including a PK data density image and a PD data density image, wherein the PK data density image reflects a density of data points corresponding to a selected dose effect and a selected time point, and the PD data density image reflects a density of data points corresponding to a selected drug effect and a selected time point; a prediction system configured to predict the set of linkage parameters using the plurality of data density images and a deep learning system, the deep learning system receiving the plurality of data density images as input and outputting the set of predicted linkage parameters, the deep learning system being trained using a simulated PK dataset and a simulated PD dataset, the simulated PK dataset being generated based on simulation of drug concentrations with respect to time points, and the simulated PD dataset being generated based on simulation of drug effects with respect to time points; and a display system communicatively connected to the computing device and configured to display a report including a predicted value for each linked parameter in the set of linked parameters.

10. 10. The system of claim 9, wherein the PK data density image is a binned intensity image, and each pixel value in at least a portion of the binned intensity image indicates a density of data points corresponding to a selected dose effect and a selected time point.

11. 10. The system of claim 9, wherein the PD data density image is a binned intensity image, and each pixel value in at least a portion of the binned intensity image indicates a density of data points corresponding to a selected dose effect and a selected time point.

12. The set of linkage parameters includes slope, half-maximal effective concentration (EC 50 ), or maximum effect (E max 10. The system of claim 9, comprising at least one of:

13. The prediction system is further configured to predict a set of PK parameters using the PK data density image, wherein the set of PK parameters includes area under the curve (AUC), minimum concentration (C min ), or maximum concentration (C max 10. The system of claim 9, comprising at least one of:

14. The system of claim 9 , wherein the deep learning system comprises a neural network system.

15. 10. The system of claim 9, wherein the deep learning system includes at least one convolutional neural network.

16. The prediction system comprises:

10. The system of claim 9, comprising a training module configured to train the deep learning system using the simulated PK data set and the simulated PD data set.

17. 1. A method for predicting a set of linked parameters related to pharmacokinetic and pharmacodynamic effects, comprising: receiving, by one or more processors, population datasets including a population pharmacokinetic (PK) dataset and a population pharmacodynamic (PD) dataset; converting, by the one or more processors, the population dataset into a plurality of binned intensity images, including a PK binned intensity image and a PD binned intensity image; predicting, by the one or more processors, the set of connectivity parameters using the plurality of binned intensity images and a deep learning system comprising at least one neural network.

18. The set of linkage parameters includes slope, half-maximal effective concentration (EC 50 ), or maximum effect (E max 20. The method of claim 17, comprising at least one of:

Images