Conditional distribution modeling as an alternative method for covariates simulation: Comparison with joint multivariate normal and bootstrap techniques

Virtual Patient Simulation Using Copula Modeling

Virtual patient simulation is increasingly performed to support model-based optimization of clinical trial designs or individualized dosing strategies. Quantitative pharmacological models typically incorporate individual-level patient characteristics, or covariates, which enable the generation of virtual patient cohorts. The individual-level patient characteristics, or covariates, used as input for such simulations should accurately reflect the values seen in real patient populations. Current methods often make unrealistic assumptions about the correlation between patient's covariates or require direct access to actual data sets with individual-level patient data, which may often be limited by data sharing limitations. We propose and evaluate the use of copulas to address current shortcomings in simulation of patient-associated covariates for virtual patient simulations for model-based dose and trial optimization in clinical pharmacology. Copulas are multivariate distribution functions that can capture joint distributions, including the correlation, of covariate sets. We compare the performance of copulas to alternative simulation strategies, and we demonstrate their utility in several case studies. Our work demonstrates that copulas can reproduce realistic patient characteristics, both in terms of individual covariates and the dependence structure between different covariates, outperforming alternative methods, in particular when aiming to reproduce high-dimensional covariate sets. In conclusion, copulas represent a versatile and generalizable approach for virtual patient simulation which preserve relationships between covariates, and offer an open science strategy to facilitate re-use of patient data sets.

Virtual patients, digital twins and causal disease models: paving the ground for in silico clinical trials

Computational models are being explored to simulate in silico the efficacy and safety of drug candidates and medical devices. Disease models that are based on patients' profiling data are being produced to represent interactomes of genes or proteins and to infer causality in the pathophysiology {AuQ: Edit OK?}, which makes it possible to mimic the impact of drugs on relevant targets. Virtual patients designed from medical records as well as digital twins were generated to simulate specific organs and to predict treatment efficacy at the individual patient level {AuQ: Edit OK?}. As the acceptance of digital evidence by regulators grows, predictive artificial intelligence (AI)-based models will support the design of confirmatory trials in humans and will accelerate the development of efficient drugs and medical devices.

Increasing transparency in machine learning through bootstrap simulation and shapely additive explanations

Machine learning methods are widely used within the medical field. However, the reliability and efficacy of these models is difficult to assess, making it difficult for researchers to identify which machine-learning model to apply to their dataset. We assessed whether variance calculations of model metrics (e.g., AUROC, Sensitivity, Specificity) through bootstrap simulation and SHapely Additive exPlanations (SHAP) could increase model transparency and improve model selection. Data from the England National Health Services Heart Disease Prediction Cohort was used. After comparison of model metrics for XGBoost, Random Forest, Artificial Neural Network, and Adaptive Boosting, XGBoost was used as the machine-learning model of choice in this study. Boost-strap simulation (N = 10,000) was used to empirically derive the distribution of model metrics and covariate Gain statistics. SHapely Additive exPlanations (SHAP) to provide explanations to machine-learning output and simulation to evaluate the variance of model accuracy metrics. For the XGBoost modeling method, we observed (through 10,000 completed simulations) that the AUROC ranged from 0.771 to 0.947, a difference of 0.176, the balanced accuracy ranged from 0.688 to 0.894, a 0.205 difference, the sensitivity ranged from 0.632 to 0.939, a 0.307 difference, and the specificity ranged from 0.595 to 0.944, a 0.394 difference. Among 10,000 simulations completed, we observed that the gain for Angina ranged from 0.225 to 0.456, a difference of 0.231, for Cholesterol ranged from 0.148 to 0.326, a difference of 0.178, for maximum heart rate (MaxHR) ranged from 0.081 to 0.200, a range of 0.119, and for Age ranged from 0.059 to 0.157, difference of 0.098. Use of simulations to empirically evaluate the variability of model metrics and explanatory algorithms to observe if covariates match the literature are necessary for increased transparency, reliability, and utility of machine learning methods. These variance statistics, combined with model accuracy statistics can help researchers identify the best model for a given dataset.

Performance of Cox proportional hazard models on recovering the ground truth of confounded exposure-response relationships for large-molecule oncology drugs

A Cox proportional hazard (CoxPH) model is conventionally used to assess exposure-response (E-R), but its performance to uncover the ground truth when only one dose level of data is available has not been systematically evaluated. We established a simulation workflow to generate realistic E-R datasets to assess the performance of the CoxPH model in recovering the E-R ground truth in various scenarios, considering two potential reasons for the confounded E-R relationship. We found that at high doses, when the pharmacological effects are largely saturated, missing important confounders is the major reason for inferring false-positive E-R relationships. At low doses, when a positive E-R slope is the ground truth, either missing important confounders or mis-specifying the interactions can lead to inaccurate estimates of the E-R slope. This work constructed a simulation workflow generally applicable to clinical datasets to generate clinically relevant simulations and provide an in-depth interpretation on the E-R relationships with confounders inferred by the conventional CoxPH model.

Efficient and relevant stepwise covariate model building for pharmacometrics

Covariate modeling is an important opportunity for pharmacometrics to influence decision making in drug development. The stepwise covariate model (SCM) building procedure is the most common method for covariate model development. Despite its advantages, the traditional SCM method is known to have long runtimes and the suboptimal ability to select relevant covariates, especially in more complex phase III settings. In this work, two alternative approaches are presented: SCM+, which introduces the “adaptive scope reduction” and changes to general estimation settings, and “stage‐wise filtering,” which groups covariates into categories based on their importance (mechanistic, structural, and exploratory). The three methods (SCM, SCM+, and SCM+ with stage‐wise filtering) are applied to data from a simulated phase III population pharmacokinetic study and are compared in terms of efficiency and relevance. The two SCM+ methods were considerably more efficient than the traditional SCM: the number of function evaluations was reduced by 70% for SCM+ and by 76% for SCM+ with stage‐wise filtering compared to SCM; the corresponding number of executed models was reduced by 44% for SCM+ and 70% for SCM+ with stage‐wise filtering. In addition, among the three methods, SCM+ with stage‐wise filtering selected the highest number of relevant covariates. Given the improved efficiency and ability to select relevant covariates shown in this work, the use of SCM+ and stage‐wise filtering can greatly increase the efficiency of covariate modeling in drug development, which will ultimately facilitate more timely support for decision making.

Lilly Absorption Modeling Platform: A Tool for Early Absorption Assessment

Oral drug absorption modeling has developed at a rapid pace in the 40 years or so since the first ideas for mathematical approaches to oral absorption were introduced. The success of compartmental approaches accelerated the uptake of absorption modeling, and over the last 20 years, work on absorption modeling has shifted almost exclusively to the compartmental framework. This report describes a new noncompartmental absorption modeling framework, the Lilly Absorption Modeling Platform (LAMP). LAMP connects a well-mixed stomach to a continuous tube model of the small intestine with plug flow. Within the continuous tube framework, the model includes intestinal mixing and a novel highly tunable precipitation model that can describe a combination of rapid nucleation and slow growth. The framework is designed to balance speed, consistency, and ease of use with a minimum of model complexity to capture the essential features of gastrointestinal (GI) physiology and critical elements of the oral absorption process. The model was validated based on predictions of the fraction absorbed and the maximum absorbable dose for a set of Eli Lilly and Company clinical compounds.