Parallel Tempering for Generation of Virtual Patients and Virtual Populations
Authors: Sheehan Robert , Myers Renee , Friedrich Christina 
Published: February 2025

Objectives: Virtual patients/mice (VPs/VMs) and virtual populations (VPops) are widely used in QSP modeling to explore the impact of variability and uncertainty on clinical response. Parallel tempering is a well-established method for parameter estimation, that offers an alternative approach to traditional methods for VM and VPop generation. This work describes an implementation of parallel tempering (PTempEst [1]) that has been adapted to calibrate a reference VM that matches multi-dimensional mechanistic data while simultaneously building a population of plausible VMs that explores the range of variability observed in the mouse data. We compared these results to a VPop generated using a random sampling approach. Methods: A previously published intracellular MAPK signaling model [2] was extended with a module describing tumor growth in a mouse xenograft model. A set of 13 tumor cell growth-related parameters were calibrated using a Bayesian parallel tempering approach; optimized via comparison to a xenograft data using multiple doses of several MAPK pathway inhibitors. A single best-fit reference VM was identified that matched the dynamics across all data sets, and a population of additional VMs was collected that fell within the measured variability in the observed data while using a different combination of parameters. For comparison, a second VPop was generated by randomly sampling values for the selected parameters from a uniform distribution, simulating across all therapies, and filtering out patients with responses outside of the data bounds. Results: Simulations of the reference virtual mouse were able to match the average dynamics of tumor decline seen across multiple doses of several MAPK pathway inhibitors, while also predicting the effects of combination therapy. The VPop consisting of hundreds of unique virtual patients was able to capture the range of observed behavior, which included a wide potential range of tumor responses. Within the population, strong and weak responders were identified and analyzed to find key drivers of responsiveness. Compared to the randomly sampled VPop, the PTempEst VPop showed more complete coverage of the sampling range and outcome range, as well as a higher yield of valid virtual patients per number of parameter sets simulated. Conclusions: Parallel tempering allows for efficient generation of virtual patient populations that are consistent with multiple sets of mechanistic constraints, capture observed variability, and fully explore the parameter space. These populations can then be used to explore patient variability in clinical response and identify key next steps to de-risk future clinical trials.Citations:[1] Gupta, S, et al. Evaluation of Parallel Tempering to Accelerate Bayesian Parameter Estimation in Systems Biology. Proceedings—26th Euromicro International Conference on Parallel, Distributed, and Network-Based Processing. (2018) [2] Sayama H, et al. Virtual clinical trial simulations for a novel KRASG12C inhibitor (ASP2453) in non-small cell lung cancer. CPT Pharmacometrics Syst Pharmacol. (2021)