Computational models for predicting hazard ratios

Abstract

Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for generating a predicted hazard ratio at an interim time point in a clinical trial. The method includes obtaining interim clinical trial data for patients, fitting a non-linear joint model to the data, and generating a collection of simulated hazard ratios using the model. For each simulated hazard ratio, patient-specific feature arrays are stochastically sampled from probability distributions parametrized by model parameters. The simulated hazard ratios are generated using the patient-specific feature arrays. A predicted hazard ratio is then generated based on a measure of central tendency of the simulated hazard ratios.

Description

Attorney Docket No. 46567-1689WO1 COMPUTATIONAL MODELS FOR PREDICTING HAZARD RATIOSCROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims priority to US Provisional Application 63 / 755,108, filed on February 6, 2025, and EP Application No. 25315112.0, filed on April 1, 2025, the disclosures of both of which are hereby incorporated by reference in their entirety.BACKGROUND

[0002] This specification relates to predicting hazard ratios for clinical trials using non-linear joint models.

[0003] Clinical trials are essential in evaluating the safety and efficacy of new medical treatments, including drugs, devices, and therapies. These trials typically proceed through phased stages, from early assessments in small patient groups (Phase I) to large-scale efficacy studies (Phase III). Time-to-event data, such as progression-free survival or overall survival, and longitudinal measurements, like biomarker levels or tumor size, are often collected to analyze treatment outcomes.

[0004] Hazard ratios are widely used in clinical research to compare the risk of an event, such as disease progression or death, between two groups over time. A hazard ratio quantifies the relative risk, with values less than one indicating reduced risk in the treatment group and values greater than one indicating increased risk. This metric provides a concise, interpretable measure of treatment efficacy and is a key endpoint in many clinical trials.SUMMARY

[0005] This specification generally describes a system implemented as computer programs on one or more computers in one or more locations that can predict a hazard ratio at an interim time point in a clinical trial.

[0006] According to one aspect, there is provided a method performed by one or more computers, the method comprising: generating a predicted hazard ratio at an interim time point in a clinical trial, comprising: obtaining interim clinical trial data for each of a plurality of patients included in the clinical trial as of the interim time point; performing a numerical optimization to fit a non-linear joint model to the interim clinical trial data, wherein the non-linear joint model isAttorney Docket No. 46567-1689WO1 configured to process a model input that comprises: (i) patient data characterizing an input patient, and (ii) a target time point, in accordance with values of a set of non-linear joint model parameters, to generate a predicted risk of a specific event occurring to the input patient at the target time point; and generating a collection of simulated hazard ratios for the clinical trial using the non-linear joint model, comprising, for each simulated hazard ratio: stochastically sampling, for each of the plurality of patients included in the clinical trial, a respective patient-specific feature array from a patient-specific probability distribution that is parametrized in part by parameters of the non-linear joint model; and generating the simulated hazard ratio using the patient-specific feature arrays for the patients included in the clinical trial; and generating the predicted hazard ratio based on a measure of central tendency of the collection of simulated hazard ratios; and outputting the predicted hazard ratio.

[0007] In some implementations, for each simulated hazard ratio, generating the simulated hazard ratio using the patient-specific feature arrays for the patients included in the clinical comprises: generating a simulation of the clinical trial using: (i) the non-linear joint model, and (ii) the patient-specific feature arrays for the plurality of patients included in the clinical trial; and generating the simulated hazard ratio based on the simulation of the clinical trial.

[0008] In some implementations, generating the simulation of the clinical trial using: (i) the non-linear joint model, and (ii) the patient-specific feature arrays for the plurality of patients included in the clinical trial comprises, for each of the plurality of patients: generating simulated longitudinal data for the patient using a longitudinal model that is included in the non-linear joint model and is dependent upon the patient-specific feature array for the patient, wherein the simulated longitudinal data comprises a respective simulated measurement of a biomedical feature of the patient at each of a plurality of time points after the interim time point.

[0009] In some implementations, generating the simulation of the clinical trial using: (i) the non-linear joint model, and (ii) the patient-specific feature arrays for the plurality of patients included in the clinical trial further comprises, for each of the plurality of patients: jointly generating a simulated event time for the patient along with the simulated longitudinal data for the patient using a hazard model that is included in the non-linear joint model and that is dependent upon the simulated longitudinal data for the patient, wherein the hazard model defines, for of a plurality of time points, a likelihood that a specific event occurs to the patient at the time point.Attorney Docket No. 46567-1689WO1

[0010] In some implementations, for each simulated hazard ratio and for each patient included in the clinical trial, the patient-specific probability distribution from which the patient-specific feature array for the patient is sampled is parametrized by both: (i) parameters of the non-linear joint model, and (ii) longitudinal data for the patient up to the interim time point.

[0011] In some implementations, for each simulated hazard ratio and for each patient included in the clinical trial, stochastically sampling the patient-specific feature array from the patient-specific probability distribution that is parametrized in part by parameters of the non-linear joint model comprises: performing the stochastic sampling using a Markov Chain Monte Carlo (MCMC) procedure.

[0012] In some implementations, for each simulated hazard ratio and for each patient included in the clinical trial, the patient-specific probability distribution does not have a closed form.

[0013] In some implementations, for each simulated hazard ratio and for each patient included in the clinical trial, the patient-specific probability distribution characterizes inter-individual variability and uncertainty in the patient-specific feature array for the patient.

[0014] In some implementations, fitting the non-linear joint model to the interim clinical trial data comprises, for each of one or more parameters of the non-linear joint model, determining a probability distribution over possible values of the parameter.

[0015] In some implementations, generating the collection of simulated hazard ratios for the clinical trial comprises, for each simulated hazard ratio: sampling a respective value for each of one or more parameters of the non-linear joint model in accordance with a probability distribution over possible values of the parameter that is determined during the fitting of the nonlinear joint model; and generating the simulated hazard ratio using the non-linear joint model parametrized by the sampled parameter values.

[0016] In some implementations, the simulation of the clinical trial comprises, for each of the plurality of patients in the clinical trial: (i) simulated longitudinal data for the patient, and (ii) a simulated event time for the patient.

[0017] In some implementations, the event comprises one or more of: disease progression; or symptom worsening; or disease recurrence; or death; or cause-specific death; or treatment discontinuation; or occurrence of an adverse event; or hospitalization; or loss of function; or progression free survival.Attorney Docket No. 46567-1689WO1

[0018] In some implementations, the biomedical feature of the patient comprises one or more of: tumor size; biomarker levels; blood pressure; cholesterol levels; lung function; body weight; viral load; hemoglobin levels; kidney function; cognitive scores; pain scores; tumor marker concentrations; or immune response.

[0019] In some implementations, generating the simulated hazard ratio based on the simulation of the clinical trial data comprises: fitting a Cox proportional hazard model to the simulation of the clinical trial data; and generating the simulated hazard ratio using the fitted Cox proportional hazard model.

[0020] In some implementations, generating the predicted hazard ratio as a measure of central tendency of the collection of simulated hazard ratios comprises generating the predicted hazard ratio as a median of the collection of simulated hazard ratios.

[0021] In some implementations, the method further comprises generating a confidence interval for the predicted hazard ratio based on the collection of simulated hazard ratios.

[0022] In some implementations, the confidence interval is determined at a significance level that is defined by an alpha spending function.

[0023] In some implementations, the significance level is specific to the interim time point in the clinical trial.

[0024] In some implementations, the alpha spending function is an O’Brien and Flemming (OBF) alpha spending function.

[0025] In some implementations, the interim clinical trial data as of the interim time point in the clinical trial comprises, for each of the plurality of patients in the clinical trial: time-to-event data for the patient that characterizes whether a specific event has occurred for the patient as of the time point; and longitudinal data for the patient that comprises measurements of a biomedical feature of the patient at a plurality of preceding time points.

[0026] In some implementations, the collection of simulated hazard ratios comprises at least 1000 simulated hazard ratios.

[0027] In some implementations, the clinical trial is for a drug.

[0028] In some implementations, the method further comprises determining that the clinical trial should be terminated at the interim time point based on the predicted hazard ratio.Attorney Docket No. 46567-1689WO1

[0029] In some implementations, the method further comprises generating a recommendation that the clinical trial should be terminated at the interim time point based on the predicted hazard ratio.

[0030] In some implementations, the clinical trial is terminated at the interim time point based on the predicted hazard ratio.

[0031] In some implementations, the method further comprises determining, based on the predicted hazard ratio, that a drug should not be administered to a patient.

[0032] In some implementations, the method further comprises preventing the drug from being administered to the patient.

[0033] In some implementations, the method further comprises determining that the clinical trial should be continued past the interim time point based on the predicted hazard ratio.

[0034] In some implementations, the method further comprises generating a recommendation that the clinical trial should be continued past the interim time point based on the predicted hazard ratio.

[0035] In some implementations, the method further comprises determining, based on the predicted hazard ratio, that a drug should be administered to a patient.

[0036] In some implementations, the method further comprises administering the drug to the patient.

[0037] In some implementations, outputting the predicted hazard ratio comprises one or more of: presenting the predicted hazard ratio on a display of a user device; or storing data identifying the predicted hazard ratio in a memory; or transmitting data identifying the predicted hazard ratio over a data communications network.

[0038] According to another aspect, there is provided a system comprising: one or more computers; and one or more storage devices communicatively coupled to the one or more computers, wherein the one or more storage devices store instructions that, when executed by the one or more computers, cause the one or more computers to perform operations of the methods described herein.

[0039] According to another aspect, there are provided one or more non-transitory computer storage media storing instructions that when executed by one or more computers cause the one or more computers to perform operations of the methods described herein.Attorney Docket No. 46567-1689WO1

[0040] The subject matter described in this specification can be implemented in particular embodiments so as to realize one or more of the following advantages.

[0041] Drug development is a long-term process aiming to bring novel therapies on the market. During the different phases of this process, data is collected in clinical studies to demonstrate the treatment clinical effectiveness and safety profiles of candidate drugs. This data can include longitudinal data such as, e.g., drug concentrations characterizing drug pharmacokinetics, tumor sizes, or blood biomarkers. The dynamics of the longitudinal data can be a primary early marker of efficacy and linked to long-term endpoints such as overall survival (OS) or progression-free survival (PFS).

[0042] The system described in this specification can predict a hazard ratio at an interim time point in a clinical trial using a non-linear joint model that captures the association between longitudinal data (e.g., characterizing tumor size or blood biomarker levels) and the occurrence of an event (e.g., death or disease progression). Generally, the longitudinal data characterizes one or more biomedical features that are correlated with or predicted of the event that is being modeled by the joint model. For instance, the longitudinal data can characterize tumor size in a patient while the event being modeled is progression free survival in the patient.

[0043] Generating predicted hazard ratios at interim time points enables early study modifications (e.g., to sample size or enrollment targets) or termination of the clinical trial for reasons of efficacy, futility, or safety. However, several technical issues arise when predicting hazard ratios by performing interim analysis of clinical trial data (i.e., at an interim time point). For instance, performing such interim analysis requires using data with reduced sample sizes which can result in high variance in predicted hazard ratios, a lack of stability of test statistics, and higher type I errors. The system described in this specification provides technical solutions that address these technical problems.

[0044] In more detail, the system can use a non-linear joint model to generate a collection of simulated hazard ratios for the clinical trial. To generate a simulated hazard ratio, the system can stochastically sample a respective patient-specific feature array for each patient included in the clinical trial from a patient-specific probability distribution. The patient-specific probability distribution is conditioned on both: (i) fitted parameter values of the joint model, and (ii) longitudinal data for the patient up to the interim time point. The system can then carry out a simulation of the clinical trial using the non-linear joint model, where the patient-specific featureAttorney Docket No. 46567-1689WO1 arrays are provided as inputs to the non-linear joint model and serve to capture inter- individual variability among patients included in the clinical trial. The system can then determine an overall predicted hazard ratio as a measure of central tendency (e.g., a median) of the individual simulated hazard ratios. By generating a collection of simulated hazard ratios that precisely accounts for inter-individual variability, the system can generate a predicted hazard ratio by a stable, robust process that mitigates the risks resulting from performing interim analysis (as outlined above), e.g., including reducing the risk of type I errors that may involve erroneously concluding that a therapeutic under examination in a clinical trial offers a significant benefit.

[0045] Notably, this approach differs from and complements an alternative approach of modeling inter- individual variability among patients by random effects that are sampled from generic probability distributions, i.e., rather than patient-specific probability distributions that are conditioned on patient-specific longitudinal data. Modeling inter-individual variability using patient-specific conditional probability distributions ties the simulation of the clinical trial more closely to the particular characteristics of the patients included in the clinical trial and enables more accurate simulation.

[0046] Further, as part of fitting the non-linear joint model, the system can determine respective probability distributions over possible values of the certain parameters of the nonlinear joint model. These probability distributions reflect underlying uncertainty in the parameter values of the joint model that result at least in part from the limited clinical trial data available during the interim analysis. Generating probability distributions over possible values of parameters of the non-linear joint model contrasts to an approach of, e.g., generating a single point estimate for each parameter value, which does not capture the uncertainty in the parameter value estimation. The system can perform each simulation of the clinical trial (e.g., as outlined above) using a respective stochastically sampled values of the non-linear joint model parameters that are specific to the particular simulation, thus further mitigating the risks of performing interim analysis, e.g., including reducing the risk of type I errors that may involve erroneously concluding that a therapeutic under examination in a clinical trial offers a significant benefit.

[0047] Further, the system can generate a confidence estimate in the predicted hazard ratio, e.g., by determining a confidence interval around the predicted hazard ratio based on the collection of simulated hazard ratios. The system can reduce the risk of type I errors by determining the confidence interval at a significance level that is defined by an alpha spendingAttorney Docket No. 46567-1689WO1 function. More specifically, by using the alpha spending function, the system can control the overall type I error rate when performing multiple interim analyses, i.e., at multiple time points throughout the clinical trial. By allocating portions of the total alpha (e.g., 0.05) to each interim analysis, the system can prevent inflation of the error rate that could occur from repeated testing.

[0048] In certain implementations, the system can generate predicted hazard ratios that are used to determine whether patients enrolled in a clinical trial should continue to be administered a drug as part of the clinical trial. Generally, the determination of whether to continue administering a drug to a patient can depend on other data points as well, e.g., including input from a healthcare provider (clinician) for the patient.

[0049] The details of one or more embodiments of the subject matter of this specification are set forth in the accompanying drawings and the description below. Other features, aspects, and advantages of the subject matter will become apparent from the description, the drawings, and the claims.BRIEF DESCRIPTION OF FIGURES

[0050] FIG. 1 illustrates a process for using computational models to estimate hazard ratios for clinical trials.

[0051] FIG. 2 illustrates an example prediction system.

[0052] FIG. 3 is a flow diagram illustrating an example process for generating a predicted hazard ratio.

[0053] FIG. 4A shows a comparison of error rates of different computational techniques used to analyze simulated clinical trial data.

[0054] FIG. 4B shows a comparison of power estimates of different computational techniques for analyzing simulated clinical trial data.

[0055] FIG. 5 shows hazard ratio estimates and confidence intervals obtained using different computational techniques from clinical trial data.

[0056] Like reference numbers and designations in the various drawings indicate like elements.DETAILED DESCRIPTION

[0057] Drug development is a lengthy process where clinical studies collect data, including longitudinal data like drug concentrations or biomarker levels, to assess the effectiveness andAttorney Docket No. 46567-1689WO1 safety of new therapies. This specification describes techniques that leverage a nonlinear joint model to predict hazard ratios at interim points in clinical trials by modeling the relationship between longitudinal biomedical features and event outcomes, such as disease progression. This approach enables informed early trial modifications or termination decisions based on efficacy, futility, or safety. In particular, the described techniques provide technical solutions that mitigate challenges in interim analysis, such as inadequate sample sizes that can lead to instability and increased errors in hazard ratio estimation. By incorporating both patient-specific variability and uncertainty through simulation-based modeling, the system enables more robust and reliable early decision-making in clinical trial management.

[0058] FIG. 1 illustrates an overview of a process for using computational models to estimate hazard ratios for clinical trials. A prediction system 200 is implemented with one or more computers for predicting hazard ratios. The prediction system 200 receives interim clinical trial data 110. The interim clinical trial data 110 can include information collected from a plurality of patients at an interim time point during the clinical trial.

[0059] In this Specification, a clinical trial can refer to a structured research study conducted to evaluate the safety and effectiveness of a medical treatment, such as a new drug, device, or other therapeutic intervention. Participants are typically assigned to one or more treatment groups, and their health outcomes are monitored over a defined period. An interim time point can refer to a designated time point during the course of the trial and prior to its planned completion, at which collected data can be analyzed to assess early signals of efficacy and / or safety. Clinical trial data collected up to the interim time point can include a variety of information, such as patient demographics, treatment assignments, longitudinal biomarker measurements (e.g., tumor size or blood protein levels), drug exposure levels, and time-to-event outcomes like disease progression or death.

[0060] The prediction system 200 processes the interim clinical trial data 110 to generate a predicted hazard ratio 220. In this Specification, a hazard ratio can refer to a statistical measure that compares the hazard, or risk, of a clinical event, such as disease progression, recurrence, or death, between two treatment groups over time. A hazard ratio less than one typically indicates a lower risk in the treatment group relative to the control group, while a hazard ratio greater than one suggests a higher risk.Attorney Docket No. 46567-1689WO1

[0061] In some cases, the predicted hazard ratio 220 can be generated at the interim time point in the clinical trial. The predicted hazard ratio 220 can provide an estimate of the relative benefits and / or risks between different treatment groups in the clinical trial. This prediction supports early decision-making by estimating the likelihood of a clinical event, such as disease progression or death, occurring in one treatment group relative to another. Details of generating the predicted hazard ratio 220 will be further described with references to FIGs. 2 and 3. In general, the prediction system 200 can perform simulations based on a nonlinear joint model that captures the relationship between longitudinal data (e.g., tumor measurements or biomarker levels) and time-to-event outcomes (e.g., progression-free survival), using the interim clinical trial data 110 to generate the predicted hazard ratio 220.

[0062] The prediction system 200 can output the predicted hazard ratio 220 in various ways. In some cases, the prediction system 200 can display the predicted hazard ratio 220 on a screen, store it in a database, or transmit it to other systems for further analysis or decision-making.

[0063] In some cases, the predicted hazard ratio 220 can be used to inform treatment decisions 120. In some cases, the predicted hazard ratio 220 can be used to determine whether to terminate or continue the clinical trial. For example, if the predicted hazard ratio 220 indicates a strong benefit for one treatment group, a decision can be made to terminate the trial early for efficacy.

[0064] Based on the treatment decisions 120, a treatment intervention 130 can be administered to a subject 140. In some cases, the predicted hazard ratio 220 can be used to determine whether to administer or not administer a drug to the subject 140. For instance, if the predicted hazard ratio 220 suggests a significant benefit for a particular drug, the treatment intervention 130 can involve administering that drug to the subject 140.

[0065] The process 100 illustrates how the prediction system 200's analysis of interim clinical trial data 110 can lead to practical clinical applications in patient care, potentially improving the efficiency and effectiveness of clinical trials.

[0066] FIG. 2 illustrates a prediction system 200 for predicting hazard ratios from interim clinical trial data. The prediction system 200 comprises one or more computers and one or more storage devices communicatively coupled to the one or more computers. The one or more storage devices store instructions that, when executed by the one or more computers, cause the one or more computers to perform operations for generating the predicted hazard ratio 220 based on the interim clinical trial data 110 using the non-linear joint model 150 and the simulation engine 230.Attorney Docket No. 46567-1689WO1

[0067] The prediction system 200 receives the interim clinical trial data 110 as input. The optimization engine 230 processes the data 110 to determine parameters 155 for the non-linear joint model 150, e.g., by performing a numerical optimization to fit the non-linear joint model 150 to the interim clinical trial data 110.

[0068] In general, the non-linear joint model 150 includes a longitudinal model that models the change in a biomarker over time and a hazard model that models the risk of an event occurring. The non-linear joint model 150 differs from classical hazard models by defining the individual risk of an event conditionally to a function of the individual random effect estimates from a mixed-effects model that describes the longitudinal data of a biomarker of interest.

[0069] The non-linear joint model 150 can be a nonlinear mixed-effects model (NLMEM) to characterize the biomarker dynamic central trend and inter-individual variability (ITV) in the population under study in the clinical trial. The following formulations provide illustrative examples of particular forms for the non-linear joint model.

[0070] Let Xtand denote the time-to-event and the censoring time for the ithsubject in the clinical trial, respectively. The time-to-event refers to the time at which a clinical event occurs, while the censoring time represents the time at which follow-up ended without observing the event. In clinical trials, not all patients are observed for the entire duration of the study, and the censoring time can indicate a time at which a patient's data is no longer included in the analysis. This can happen for various reasons, such as a patient withdrawing from the study, being lost to follow-up, or the study ending before the event of interest occurs for that patient.

[0071] For each subject i, the survival data are observed and represented as (7), 6i with Tt= min( j, Ci) and 8tthe event indicator. 6i = 1 if the patient experienced the event at time Tt, and 6t = 0 otherwise. The instantaneous risk of the event for individual i can be defined by:hi(t | Zt, Trt) = S0 if t-0mh0(t) x exp( / ?sx Zt+ pTr'X. Tri) if t > 0Jwhere h0(t) is the baseline hazard function, representing the instantaneous risk over time without the influence of any covariates, with t denoting the time elapsed since baseline (treatment initiation in the following). / ?sis the vector of coefficients associated with the individual i baseline covariate vector Zt and ftTris the coefficient associated with the treatment arm indicator Trt. In a fully parametric joint model, the baseline hazard function h0(t) is defined with a parametric form, and a parameter vector y is estimated as part of the model.Attorney Docket No. 46567-1689WO1

[0072] Let ytj denote the longitudinal biomarker level of individual i observed at measurement time ttj where i E {1;...; N with N the total number of individuals, and J E {1;...; n with ntthe number of measurements for patient i. The longitudinal biomarker trajectory is modeled as:ytj = + g^tij^i^^Cij (2)

[0073] The functiondescribes the structural model capturing the nonlinear dynamics of the biomarker. The vector ip contains individual-specific parameters, which follow a distribution T based on biological assumptions. One example is:= T( / I) + T]t + Pi X where g is the vector of fixed effects (population means), Th ~ N (0, fl) represents the interindividual random effect vector for subject i with fl being a variance-covariance matrix. Inter-individual variability can be partly explained by baseline covariates Wtwith / ?; being the vector of associated coefficients. The error model g ttj W / f) defines the variability of the residual errors ~ N (0,1) with representing the vector of error model parameters.

[0074] In the nonlinear joint model, the hazard function is extended to incorporate the evolving biomarker process. The instantaneous risk is expressed as:z z A A (° if t < 0 hi(.t | MifalpiM. Zi) -x expQgs x Z.+pM xf(tjy.)} ift> o

[0075] Here,M^t, WP) = (m(u, WP); 0 < u < t represents the nonlinear longitudinal process of the biomarker of interest up to time t (where t > 0 ), and f(t, ipi, Vl / J is a link function that relates the biomarker dynamics to the risk. The coefficientMrepresents the strength of the relationship between f(t, ipi, Vl / J and the time-to-event process. The nonlinear joint model (Eq. 3) allows the model to incorporate both baseline covariatessXand time-dependent biomarker informationMX f(t, ipi, VkJ into the estimation of event risk.

[0076] Using the nonlinear joint model 150 offers several key advantages over traditional hazard ratio analysis methods, particularly in the context of clinical trials that involve rich longitudinal biomarker data. Unlike classical models such as the Cox proportional hazards model, which consider only time-to-event outcomes, the nonlinear joint model 150 integrates both longitudinal data (e.g., tumor size, biomarker levels) and time-to-event data (e.g., progression, death) within a unified framework. This integration allows the model to capture complex, individualized disease dynamics and the evolving effect of treatment over time. ByAttorney Docket No. 46567-1689WO1 directly modeling the relationship between biomarker trajectories and survival outcomes, the nonlinear joint model provides a more nuanced and biologically informed estimate of event risk.

[0077] In addition, the nonlinear joint model accounts for both inter-individual variability and estimation uncertainty, making it particularly effective for interim analyses in clinical trials where data may be incomplete or noisy. As further described below, during simulations, the model can generate a distribution of plausible future outcomes by sampling patient-specific parameters and hazard model coefficients. This enables robust prediction of hazard ratios even when only partial trial data is available, supporting earlier and more confident decision-making.

[0078] Any appropriate optimization techniques can be used to determine the parameters 155. Examples of optimization techniques include gradient descent, Newton-Raphson, expectationmaximization (EM) algorithms, stochastic approximation expectation maximization (SAEM), and Bayesian estimation techniques.

[0079] In some cases, the optimization engine 230 determines a probability distribution over possible values for each of one or more of the parameters 155. That is, instead of computing a single point estimate for a model parameter, the optimization engine 230 can estimate a distribution that reflects the uncertainty associated with that parameter's value, based on the available interim clinical trial data 110.

[0080] For example, the optimization engine 230 can model the parameter values as being drawn from a multivariate normal distribution characterized by a mean vector and a variancecovariance matrix, where the mean corresponds to the estimated parameter values and the covariance captures inter-parameter uncertainty and correlations. As will be described below, determining probability distributions over possible parameter values enables the prediction system 200 to account for model uncertainty during simulations by sampling parameter sets from these distributions when generating simulated hazard ratios.

[0081] After the parameter values of the model parameters 155 have been determined, the simulation engine 230 uses the non-linear joint model 150 to generate a collection of simulated hazard ratios 240 based on the interim clinical trial data 110. The clinical trial data 110 includes longitudinal data, such as biomarker levels or tumor sizes, and time-to-event data, such as progression-free survival or overall survival, for a set of patients up to an interim time point. Each simulated hazard ratio 240 is generated by performing a simulation based on virtual patients derived from the set of patients included in the clinical trial.Attorney Docket No. 46567-1689WO1

[0082] In particular, for each simulated hazard ratio 240, the simulation engine 230 simulates virtual patients by stochastically sampling patient-specific features from patient-specific probability distributions for the set of patients included in the trial. The simulation engine 230 generates the simulated hazard ratio 240 using the sampled patient-specific feature parameters. In other words, the simulation engine uses the sampled patient parameters as input to the nonlinear joint model to predict a hazard ratio for that particular simulation.

[0083] The simulation engine 230 generates the simulated hazard ratio 240 using these sampled patient-specific feature parameters to simulate future biomarker trajectories and event times for each virtual patient, and fitting a hazard model to the simulated outcomes across treatment groups. An example of the hazard model is the Cox model, which estimates the hazard ratio by comparing the event risk over time between treatment groups, while accounting for censored data.

[0084] As such, each simulated hazard ratio 240 reflects a complete, plausible future outcome of the trial, based on the observed interim data and model-informed uncertainty in both patientlevel dynamics and treatment effects. This process is repeated multiple times to generate the collection of simulated hazard ratios 240, which can be used to estimate a predicted hazard ratio 230 and assess the likely outcome of the clinical trial.

[0085] The simulation engine 230 generates each simulated hazard ratio 240 by simulating a future outcome of the clinical trial using (i) the nonlinear joint model 150 and (ii) the patientspecific feature arrays sampled for the patients in the trial. Each simulation reflects a hypothetical future progression of the trial, starting from the interim time point and incorporating both the biomarker dynamics and the likelihood of clinical events.

[0086] The simulation engine 230 uses the nonlinear joint model 150 to generate, for each patient, a personalized trajectory of the biomedical feature of interest, such as tumor size or a relevant biomarker, based on the sampled feature array. The simulation of each patient’s future biomarker trajectory can be carried out by a longitudinal model of the nonlinear joint model 150. This model uses the patient-specific feature array to generate simulated longitudinal data that represents expected measurements of the biomarker at multiple future time points beyond the interim time point. These biomarker trajectories serve as individualized, time-dependent predictors of clinical outcomes.Attorney Docket No. 46567-1689WO1

[0087] The simulation engine 230 uses a hazard model of the nonlinear joint model 150 to generate a simulated event time for each virtual patient. The hazard model accounts for the timevarying simulated biomarker values when estimating the patient’s risk of experiencing an event, such as disease progression, symptom worsening, or death. The hazard function provides a likelihood of event occurrence at each time point, conditioned on the patient’s biomarker profile, treatment assignment, and baseline covariates.

[0088] The simulation engine 230 can sample the patient-specific feature arrays for each virtual patient from probability distributions parameterized by both (i) the nonlinear joint model parameters and (ii) the patient’s observed longitudinal data up to the interim time point. These distributions capture inter-individual variability in disease dynamics and uncertainty in parameter estimation due to limited interim data. In some cases, these distributions typically do not have a closed-form expression. The simulation engine 230 can use stochastic methods, such as Markov Chain Monte Carlo (MCMC), to perform the sampling.

[0089] By incorporating both inter-individual variability and statistical uncertainty, the patientspecific distributions used in simulation allow each virtual patient to reflect a biologically plausible yet uncertain outcome pathway. This individualized simulation framework enhances realism and robustness in hazard ratio prediction.

[0090] In some implementations, the simulation engine 230 also accounts for uncertainty in the nonlinear joint model itself by sampling one or more model parameters from estimated probability distributions during simulation. For example, the engine can sample hazard model parameters from a multivariate normal distribution defined by the mean parameter estimates and their variance-covariance matrix obtained during model fitting. This approach propagates modellevel uncertainty into the generation of simulated hazard ratios, further improving the reliability of the predicted hazard ratio.

[0091] Each simulation thus produces, for every patient, (i) a simulated longitudinal biomarker trajectory and (ii) a simulated time-to-event, which together constitute a fully simulated clinical trial outcome. The collection of these individual outcomes across treatment arms is then used to fit a hazard model, such as the Cox proportional hazards model, to compute the simulated hazard ratio 240.

[0092] Repeating this process multiple times produces a distribution of simulated hazard ratios that captures both individual-level and model-level uncertainty. The prediction system 200Attorney Docket No. 46567-1689WO1 aggregates this distribution (e.g., by computing a measure of central tendency such as the median) to generate a predicted hazard ratio 220. This predicted hazard ratio can then be used to assess the likely outcome of the clinical trial and support early decision-making, such as stopping the trial for efficacy or futility, or adjusting trial parameters like enrollment targets.

[0093] In an illustrative example of the simulation process, for an ongoing clinical trial at a given time t, observed longitudinal and hazard data from multiple treatment arms are available for the set of patients in the trial. The non-linear joint model includes of a treatment arm-specific non-linear model sharing random effects with a common parametric proportional hazard model. Therefore, it assumes that all patients share the same baseline hazard h0(t).

[0094] The population parameter estimates 0jMcan be used to sample d E {1;...; D vectors of individual parameters i tddrawn from the conditional distribution p^ipiI AG while D vectors of hazard parameters are sampled from a multivariate normal distribution 9s d~N ()s, Var(0s)), with Var(0s) the associated estimation variance covariance matrix.

[0095] Then the simulation engine 230 can use the sampled patient-specific parametersdand survival model parameters 9s din the joint model to simulate a dataset of longitudinal and hazard data until the study completion (as defined in the protocol, i.e. typically when the total number of expected events is reached). This simulation can be repeated D times. The generated hazard data from each dataset can be analyzed with a Cox model to provide a distribution of D simulated hazard rates 240.

[0096] The event modeled in the simulation can represent a wide range of clinically meaningful outcomes, including but not limited to: disease progression, symptom worsening, disease recurrence, death, cause-specific death, treatment discontinuation, adverse event occurrence, hospitalization, loss of function, or progression-free survival. Likewise, the biomedical feature modeled by the longitudinal model can include one or more of: tumor size, biomarker levels, blood pressure, cholesterol levels, lung function, body weight, viral load, hemoglobin levels, kidney function, cognitive scores, pain scores, tumor marker concentrations, or immune response. This flexibility allows the system to be adapted to a broad array of clinical contexts and therapeutic domains.

[0097] In a particular illustrative example, the longitudinal model models tumor growth inhibition (TGI) as:Attorney Docket No. 46567-1689WO1rM0Trx exp(KgTrx t) if t < Tstart= • / KsTr / , (4) M0Trx exp I KgTrx t - 11 — exp(— RTr(t — Tstart)) 1 I otherwisek \ Rrrv JJ

[0098] Before treatment initiation (when t < Tstart), biomarker levels increased exponentially over time at a rate KgTr, relative to the baseline biomarker levels M0Tr. After treatment initiation, biomarker levels varied according to the drug-dependent tumor shrinkage rate KsTrand the rate of development of treatment resistance RTr. It is assumed that the individual parameters followed a log-normal distribution, such that log(i> = log( / r) + rg. The random effects r / i are assumed to be normally distributed with a mean of zero and a diagonal variancecovariance matrix j]t~ N (0, fl) ). A proportional error model can be used to describe the variability of the residual errors etj, which is assumed to be independently and identically distributed according to a standard normal distribution. In equation 2. this was expressed as= b x where b is the proportional residual error term.

[0099] The hazard model can adopt a Weibull proportional hazard model as the baseline hazard function with K and A as the shape and scale parameters, respectively, and the slope of the simulated longitudinal process of the biomarkerasthe link function. Thus, theindividual instantaneous risk of an event is described as:if t < Tstart| Mf(t,i / >f)) K / (t - 7’start )V1(5)Tx- i - x exp / ?Mx - — - afterA \ A / \ at

[0100] Here 0jM={0;, TEST> $Z, REF> b, $s} is the vector of nonlinear joint model parameters to be estimated. 0^TEST=0TEST, Kg-TEST > ^STEST > ^TEST > 0TEST> ’ ^RTEST J’0tREF—{M0REF, K £REF K SREF, 7?REF, toMoREF, ^i<gREP> " KSREF > " RREF }are thevectors of longitudinal structural model parameters related to test treatment arm (TEST) and reference treatment arm(REF), respectively, b is the proportional residual error term, and 0S= {K, A,M} is the vector of hazard model parameters.

[0101] Once the collection of simulated hazard ratios 240 have been computed, the system 200 can generate the predicted hazard ratio 220 based on a measure of central tendency of the collection of simulated hazard ratios. For example, the system 200 can identify the median of theAttorney Docket No. 46567-1689WO1 simulated hazard ratios 240 as the predicted hazard ratio 220. In another example, the system 200 can calculate the mean of the simulated hazard ratios 240 as the predicted hazard ratio 220. Other statistical measures, such as a trimmed mean or mode, can be used depending on the characteristics of the distribution and the goals of the analysis. In some cases, the system 200 can determine a confidence level of the predicted hazard ratio 220 based on the distribution of the simulated hazard ratios 240. For example, the system 200 can compute a confidence interval for the predicted hazard ratio 220 based on quantiles of the collection of simulated hazard ratios 240.

[0102] The system 200 can output the predicted hazard ratio 220 in a variety of ways. For example, the system 200 can present the predicted hazard ratio 220 on a display of a user device. In another example, the system 200 can store data identifying the predicted hazard ratio 220 in a storage device. In yet another example, the system 200 can transmit data identifying the predicted hazard ratio 220 over a data communications network.

[0103] As described with reference to FIG. 1, the predicted hazard ratio 220 can be used to inform treatment decisions 120, such as whether to continue, modify, or terminate the clinical trial. For instance, a predicted hazard ratio indicating a significantly increased risk of adverse outcomes may support early termination of the trial to minimize patient risk and ensure participant safety.

[0104] FIG. 3 is a flow diagram of an example process 300 for generating a predicted hazard ratio from clinical trial data. For convenience, the process 300 will be described as being performed by a system of one or more computers located in one or more locations. For example, a prediction system, e.g., the prediction system 200 of FIG. 2, appropriately programmed in accordance with this specification, can perform the process 300.

[0105] At 310, the system obtains interim clinical trial data. The interim clinical trial data includes information collected from a plurality of patients at an interim time point during the clinical trial.

[0106] At 320, the system determines parameters of a nonlinear joint model. This involves performing a numerical optimization to fit the nonlinear joint model to the interim clinical trial data. The non-linear joint model is configured to process a model input that includes (i) patient data characterizing an input patient and (ii) a target time point, in accordance with values of a set of non-linear joint model parameters, to generate a predicted risk of a specific event occurring to the input patient at the target time point.Attorney Docket No. 46567-1689WO1

[0107] The system then generates a collection of simulated hazard ratios for the clinical trial using the non-linear joint model. In particular, the system performs 330 and 340 to compute each simulated hazard ratio.

[0108] At step 330, the system samples patient-specific feature arrays. For each patient included in the clinical trial, the system stochastically samples a patient-specific feature array from a probability distribution for that patient. This distribution can be parameterized by both (i) the fitted parameters of the nonlinear joint model and (ii) the patient’s longitudinal data up to the interim time point. The patient-specific distribution can characterize inter-individual variability and uncertainty in the feature array.

[0109] In some cases, the patient-specific probability distribution does not have a closed form. The system can perform the stochastic sampling using a Markov Chain Monte Carlo (MCMC) procedure.

[0110] At 340, the system generates a simulated hazard ratio using the patient-specific feature arrays for the patients included in the clinical trial.

[0111] In some implementations, to generate the simulated hazard ratio, the system generates a simulation of the clinical trial using: (i) the non-linear joint model, and (ii) the patient-specific feature arrays for the plurality of patients included in the clinical trial, and generates the simulated hazard ratio based on the simulation of the clinical trial.

[0112] In particular, the system can perform the simulation of the clinical trial by, for each of the set of patients included in the clinical trial, generating simulated longitudinal data for the patient using a longitudinal model that is included in the non-linear joint model and is dependent upon the patient-specific feature array for the patient. The simulated longitudinal data can include a respective simulated measurement of a biomedical feature of the patient at each of a plurality of time points after the interim time point.

[0113] In some cases, the system can jointly generate a simulated event time for the patient along with the simulated longitudinal data for the patient using a hazard model that is included in the non-linear joint model and that is dependent upon the simulated longitudinal data for the patient. The hazard model defines, for a plurality of time points, a likelihood that a specific event occurs to the patient at the time point.Attorney Docket No. 46567-1689WO1

[0114] The patient-specific probability distribution from which the patient-specific feature array for the patient is sampled can be parametrized by both: (i) parameters of the non-linear joint model, and (ii) longitudinal data for the patient up to the interim time point.

[0115] In some cases, the system can also sample values for one or more parameters of the nonlinear joint model for each simulation run, using probability distributions that were determined during the model-fitting step. This accounts for model-level uncertainty.

[0116] The system repeats steps 330 and 340 to generate multiple simulated hazard ratios, forming a collection of simulated hazard ratios for the clinical trial.

[0117] At 350, the system generates a predicted hazard ratio based on a measure of central tendency of the simulated hazard ratio distribution. For example, the system can compute the median or mean of the collection as the predicted hazard ratio. Thus, the predicted hazard ratio can represent a typical or average hazard ratio expected in the clinical trial, based on the simulations of virtual trials that account for the variability among individual patients and in some cases, the uncertainty inherent in the model parameters.

[0118] At 360, the system outputs the predicted hazard ratio 220. This can involve displaying the predicted hazard ratio on a user device, storing it in a memory or database, or transmitting it over a communications network for downstream use.

[0119] FIG. 4A shows a comparison of different methods for estimating hazard ratios at various analysis timepoints in a clinical trial simulation study conducted under the null hypothesis — that is, assuming no true treatment effect exists. The table includes results for the Cox model fitted to observed data (Coxobs), a parametric model fitted to observed data (Paramobs), a Cox model with simulations (Coxsim), a parametric model with simulations (Paramsim), and the techniques described above which uses simulations based on the non-linear joint model (JM). For each method, the table presents the global type I error rate and its associated 95% confidence interval, calculated across 1,000 simulated trials.

[0120] In some cases, simulations using the nonlinear joint model can provide more controlled and reliable estimates of the hazard ratio compared to other methods, as evidenced by the alignment of the type I error rate with the nominal threshold (e.g., 2.5%). For example, at the final analysis, the joint model approach yields a type I error rate that is both close to the nominal value and within a narrow confidence interval, whereas the parametric simulation approach shows greater variability and tends to be overly conservative. This highlights the ability of theAttorney Docket No. 46567-1689WO1 nonlinear joint model to maintain statistical validity while incorporating longitudinal data and simulation-based inference.

[0121] FIG. 4B shows another comparison of different methods for estimating hazard ratios at various analysis timepoints in a clinical trial simulation study conducted under the alternative hypothesis — that is, assuming a true treatment effect exists. The table presents the statistical power of each method, measured as the proportion of simulated trials in which the method correctly detects a treatment effect (i.e., produces a significant hazard ratio). For each method and timepoint (e.g., first interim, second interim, final analysis), the table also includes 95% confidence intervals for the power estimates, based on 1,000 simulated trials.

[0122] In some cases, simulations using the nonlinear joint model can provide substantially higher statistical power compared to other methods, especially at early interim timepoints, as evidenced by a greater proportion of correctly identified treatment effects. For example, at the first interim analysis, the joint model approach demonstrates more than twice the power of the traditional Cox model, indicating a much greater likelihood of detecting early treatment benefit. This highlights the ability of the nonlinear joint model to leverage longitudinal biomarker data and individualized patient modeling to produce more sensitive and timely hazard ratio estimates, which can support faster and more confident decision-making in clinical trials.

[0123] FIG. 5 shows hazard ratio estimates and their confidence intervals obtained using different computational techniques from clinical trial data of the ICARIA-MM study, which is a Phase 3 clinical trial to evaluate the efficacy of the Isa-Pd combination compared to Pd for the treatment of relapsed and refractory multiple myeloma (RRMM) patients. The figure displays the results at multiple analysis timepoints — such as the 1st interim, 2nd interim, and final analysis — for each method. Each estimate is accompanied by a (1-2α)×100% confidence interval, where a is the significance level defined by the O'Brien and Fleming (OBF) function.

[0124] The figure illustrates that the joint model approach can provide more stable hazard ratio estimates across timepoints. For example, while the joint model did not reach significance at the 1st interim analysis, at the 2nd interim analysis and final analyses, it provided a PFS HR estimate slightly significantly lower than 1.

[0125] Embodiments of the subject matter and the functional operations described in this specification can be implemented in digital electronic circuitry, in tangibly-embodied computer software or firmware, in computer hardware, including the structures disclosed in thisAttorney Docket No. 46567-1689WO1 specification and their structural equivalents, or in combinations of one or more of them.Embodiments of the subject matter described in this specification can be implemented as one or more computer programs, i.e., one or more modules of computer program instructions encoded on a tangible non transitory storage medium for execution by, or to control the operation of, data processing apparatus. The computer storage medium can be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, or a combination of one or more of them. Alternatively or in addition, the program instructions can be encoded on an artificially generated propagated signal, e.g., a machine-generated electrical, optical, or electromagnetic signal, that is generated to encode information for transmission to suitable receiver apparatus for execution by a data processing apparatus.

[0126] The term “data processing apparatus” refers to data processing hardware and encompasses all kinds of apparatus, devices, and machines for processing data, including by way of example a programmable processor, a computer, or multiple processors or computers. The apparatus can also be, or further include, special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit). The apparatus can optionally include, in addition to hardware, code that creates an execution environment for computer programs, e.g., code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of one or more of them.

[0127] A computer program, which may also be referred to or described as a program, software, a software application, an app, a module, a software module, a script, or code, can be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages; and it can be deployed in any form, including as a stand alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A program may, but need not, correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data, e.g., one or more scripts stored in a markup language document, in a single file dedicated to the program in question, or in multiple coordinated files, e.g., files that store one or more modules, sub programs, or portions of code. A computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and interconnected by a data communication network.Attorney Docket No. 46567-1689WO1

[0128] In this specification the term “engine” is used broadly to refer to a software-based system, subsystem, or process that is programmed to perform one or more specific functions. Generally, an engine will be implemented as one or more software modules or components, installed on one or more computers in one or more locations. In some cases, one or more computers will be dedicated to a particular engine; in other cases, multiple engines can be installed and running on the same computer or computers.

[0129] The processes and logic flows described in this specification can be performed by one or more programmable computers executing one or more computer programs to perform functions by operating on input data and generating output. The processes and logic flows can also be performed by special purpose logic circuitry, e.g., an FPGA or an ASIC, or by a combination of special purpose logic circuitry and one or more programmed computers.

[0130] Computers suitable for the execution of a computer program can be based on general or special purpose microprocessors or both, or any other kind of central processing unit. Generally, a central processing unit will receive instructions and data from a read only memory or a random access memory or both. The essential elements of a computer are a central processing unit for performing or executing instructions and one or more memory devices for storing instructions and data. The central processing unit and the memory can be supplemented by, or incorporated in, special purpose logic circuitry. Generally, a computer will also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic, magneto optical disks, or optical disks. However, a computer need not have such devices. Moreover, a computer can be embedded in another device, e.g., a mobile telephone, a personal digital assistant (PDA), a mobile audio or video player, a game console, a Global Positioning System (GPS) receiver, or a portable storage device, e.g., a universal serial bus (USB) flash drive, to name just a few.

[0131] Computer readable media suitable for storing computer program instructions and data include all forms of non volatile memory, media and memory devices, including by way of example semiconductor memory devices, e.g., EPROM, EEPROM, and flash memory devices; magnetic disks, e.g., internal hard disks or removable disks; magneto optical disks; and CD ROM and DVD-ROM disks.

[0132] To provide for interaction with a user, embodiments of the subject matter described in this specification can be implemented on a computer having a display device, e.g., a CRTAttorney Docket No. 46567-1689WO1 (cathode ray tube) or LCD (liquid crystal display) monitor, for displaying information to the user and a keyboard and a pointing device, e.g., a mouse or a trackball, by which the user can provide input to the computer. Other kinds of devices can be used to provide for interaction with a user as well; for example, feedback provided to the user can be any form of sensory feedback, e.g., visual feedback, auditory feedback, or tactile feedback; and input from the user can be received in any form, including acoustic, speech, or tactile input. In addition, a computer can interact with a user by sending documents to and receiving documents from a device that is used by the user; for example, by sending web pages to a web browser on a user’s device in response to requests received from the web browser. Also, a computer can interact with a user by sending text messages or other forms of message to a personal device, e.g., a smartphone that is running a messaging application, and receiving responsive messages from the user in return.

[0133] Data processing apparatus for implementing structure prediction neural networks can also include, for example, special-purpose hardware accelerator units for processing common and compute-intensive parts of machine learning training or production, i.e., inference, workloads.

[0134] Machine learning models can be implemented and deployed using a machine learning framework, e.g., a TensorFlow framework, or a Jax framework.

[0135] Embodiments of the subject matter described in this specification can be implemented in a computing system that includes a back end component, e.g., as a data server, or that includes a middleware component, e.g., an application server, or that includes a front end component, e.g., a client computer having a graphical user interface, a web browser, or an app through which a user can interact with an implementation of the subject matter described in this specification, or any combination of one or more such back end, middleware, or front end components. The components of the system can be interconnected by any form or medium of digital data communication, e.g., a communication network. Examples of communication networks include a local area network (LAN) and a wide area network (WAN), e.g., the Internet.

[0136] The computing system can include clients and servers. A client and server are generally remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other. In some embodiments, a server transmits data, e.g., an HTML page, to a user device, e.g., for purposes of displaying data to andAttorney Docket No. 46567-1689WO1 receiving user input from a user interacting with the device, which acts as a client. Data generated at the user device, e.g., a result of the user interaction, can be received at the server from the device.

[0137] While this specification contains many specific implementation details, these should not be construed as limitations on the scope of any invention or on the scope of what may be claimed, but rather as descriptions of features that may be specific to particular embodiments of particular inventions. Certain features that are described in this specification in the context of separate embodiments can also be implemented in combination in a single embodiment.Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable subcombination. Moreover, although features may be described above as acting in certain combinations and even initially be claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a subcombination or variation of a subcombination.

[0138] Similarly, while operations are depicted in the drawings and recited in the claims in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. In certain circumstances, multitasking and parallel processing may be advantageous. Moreover, the separation of various system modules and components in the embodiments described above should not be understood as requiring such separation in all embodiments, and it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products.

[0139] Particular embodiments of the subject matter have been described. Other embodiments are within the scope of the following claims. For example, the actions recited in the claims can be performed in a different order and still achieve desirable results. As one example, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In some cases, multitasking and parallel processing maybe advantageous.What is claimed is:

Claims

1. Attorney Docket No. 46567-1689WO1CLAIMS1. A method performed by one or more computers, the method comprising:generating a predicted hazard ratio at an interim time point in a clinical trial, comprising:obtaining interim clinical trial data for each of a plurality of patients included in the clinical trial as of the interim time point;performing a numerical optimization to fit a non-linear joint model to the interim clinical trial data, wherein the non-linear joint model is configured to process a model input that comprises: (i) patient data characterizing an input patient, and (ii) a target time point, in accordance with values of a set of non-linear joint model parameters, to generate a predicted risk of a specific event occurring to the input patient at the target time point; andgenerating a collection of simulated hazard ratios for the clinical trial using the non-linear joint model, comprising, for each simulated hazard ratio:stochastically sampling, for each of the plurality of patients included in the clinical trial, a respective patient-specific feature array from a patient-specific probability distribution that is parametrized in part by parameters of the non-linear joint model; and generating the simulated hazard ratio using the patient-specific feature arrays for the patients included in the clinical trial; andgenerating the predicted hazard ratio based on a measure of central tendency of the collection of simulated hazard ratios; andoutputting the predicted hazard ratio.

2. The method of claim 1, wherein for each simulated hazard ratio, generating the simulated hazard ratio using the patient-specific feature arrays for the patients included in the clinical comprises:generating a simulation of the clinical trial using: (i) the non-linear joint model, and (ii) the patient-specific feature arrays for the plurality of patients included in the clinical trial; and generating the simulated hazard ratio based on the simulation of the clinical trial.

3. The method of claim 2, wherein generating the simulation of the clinical trial using: (i) the non-linear joint model, and (ii) the patient-specific feature arrays for the plurality of patients included in the clinical trial comprises, for each of the plurality of patients:Attorney Docket No. 46567-1689WO1 generating simulated longitudinal data for the patient using a longitudinal model that is included in the non-linear joint model and is dependent upon the patient-specific feature array for the patient,wherein the simulated longitudinal data comprises a respective simulated measurement of a biomedical feature of the patient at each of a plurality of time points after the interim time point.

4. The method of claim 3, wherein generating the simulation of the clinical trial using: (i) the non-linear joint model, and (ii) the patient-specific feature arrays for the plurality of patients included in the clinical trial further comprises, for each of the plurality of patients:jointly generating a simulated event time for the patient along with the simulated longitudinal data for the patient using a hazard model that is included in the non-linear joint model and that is dependent upon the simulated longitudinal data for the patient,wherein the hazard model defines, for a plurality of time points, a likelihood that a specific event occurs to the patient at the time point.

5. The method of any one of claims 3-4, wherein for each simulated hazard ratio and for each patient included in the clinical trial, the patient-specific probability distribution from which the patient-specific feature array for the patient is sampled is parametrized by both: (i) parameters of the non-linear joint model, and (ii) longitudinal data for the patient up to the interim time point.

6. The method of any preceding claim, wherein for each simulated hazard ratio and for each patient included in the clinical trial, stochastically sampling the patient-specific feature array from the patient-specific probability distribution that is parametrized in part by parameters of the non-linear joint model comprises:performing the stochastic sampling using a Markov Chain Monte Carlo (MCMC) procedure.Attorney Docket No. 46567-1689WO1 7. The method of any preceding claim, for each simulated hazard ratio and for each patient included in the clinical trial, the patient-specific probability distribution does not have a closed form.

8. The method of any preceding claim, wherein for each simulated hazard ratio and for each patient included in the clinical trial, the patient-specific probability distribution characterizes inter-individual variability and uncertainty in the patient-specific feature array for the patient.

9. The method of any preceding claim, wherein fitting the non-linear joint model to the interim clinical trial data comprises, for each of one or more parameters of the non-linear joint model, determining a probability distribution over possible values of the parameter.

10. The method of claim 9, wherein generating the collection of simulated hazard ratios for the clinical trial comprises, for each simulated hazard ratio:sampling a respective value for each of one or more parameters of the non-linear joint model in accordance with a probability distribution over possible values of the parameter that is determined during the fitting of the non-linear joint model; andgenerating the simulated hazard ratio using the non-linear joint model parametrized by the sampled parameter values.

11. The method of any one of claims 2-10, wherein the simulation of the clinical trial comprises, for each of the plurality of patients in the clinical trial: (i) simulated longitudinal data for the patient, and (ii) a simulated event time for the patient.

12. The method of any one of claims 4-5, wherein the event comprises one or more of: disease progression; or symptom worsening; or disease recurrence; or death; or cause-specific death; or treatment discontinuation; or occurrence of an adverse event; or hospitalization; or loss of function; or progression free survival.

13. The method of any one of claims 3-5, wherein the biomedical feature of the patient comprises one or more of: tumor size; biomarker levels; blood pressure; cholesterol levels; lungAttorney Docket No. 46567-1689WO1 function; body weight; viral load; hemoglobin levels; kidney function; cognitive scores; pain scores; tumor marker concentrations; or immune response.

14. A system comprising:one or more computers; andone or more storage devices communicatively coupled to the one or more computers, wherein the one or more storage devices store instructions that, when executed by the one or more computers, cause the one or more computers to perform operations of the respective method of any one of claims 1-13.

15. One or more non-transitory computer storage media storing instructions that when executed by one or more computers cause the one or more computers to perform operations of the respective method of any one of claims 1-13.

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