Well-tempered MCMC simulations for population pharmacokinetic models

Area of Science:

• Computational Statistics
• Pharmacometrics
• Bayesian Inference

Background:

• Bayesian statistical analysis of complex pharmacokinetic/pharmacodynamic models, especially in population studies, offers powerful inference capabilities.
• Markov Chain Monte Carlo (MCMC) samplers are crucial for estimating posterior parameter distributions, but standard methods struggle with multi-modal posteriors and model selection.

Purpose of the Study:

• To implement and evaluate the Trans-dimensional Markov Chain Monte Carlo (TMCMC) algorithm for complex pharmacokinetic and pharmacodynamic models within a Bayesian framework.
• To address the challenge of selecting appropriate auxiliary inverse temperatures (perks) and scaling constants for TMCMC sampling through adaptive stochastic optimization.
• To demonstrate the utility of TMCMC for sampling sharp multi-modal posteriors, assessing model identifiability, and computing Bayes factors for model choice.

Main Methods:

• Developed an adaptive stochastic optimization method to determine optimal auxiliary inverse temperatures (perks) and scaling constants for TMCMC.
• Implemented the TMCMC sampling algorithm in the GNU MCSim software.
• Compared TMCMC performance against other samplers using stylized case studies and realistic population pharmacokinetic models, including a large physiologically-based pharmacokinetic (PBPK) model.

Main Results:

• The adaptive optimization successfully determined adequate perk grids, enabling efficient TMCMC sampling.
• TMCMC demonstrated superior performance in sampling multi-modal posteriors and calculating Bayes factors compared to other MCMC methods.
• The implemented TMCMC approach proved effective for complex population pharmacokinetic inference problems.

Conclusions:

• The TMCMC algorithm, enhanced with adaptive optimization for perk selection, provides a robust and efficient Bayesian inference tool for complex pharmacokinetic and pharmacodynamic models.
• This method facilitates accurate model selection and parameter estimation, even in the presence of challenging multi-modal posteriors and identifiability issues.
• The implementation in GNU MCSim offers a practical solution for researchers in pharmacometrics and related fields.