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Well-tempered MCMC simulations for population pharmacokinetic models

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Abstract

A full Bayesian statistical treatment of complex pharmacokinetic or pharmacodynamic models, in particular in a population context, gives access to powerful inference, including on model structure. Markov Chain Monte Carlo (MCMC) samplers are typically used to estimate the joint posterior parameter distribution of interest. Among MCMC samplers, the simulated tempering algorithm (TMCMC) has a number of advantages: it can sample from sharp multi-modal posteriors; it provides insight into identifiability issues useful for model simplification; it can be used to compute accurate Bayes factors for model choice; the simulated Markov chains mix quickly and have assured convergence in certain conditions. The main challenge when implementing this approach is to find an adequate scale of auxiliary inverse temperatures (perks) and associated scaling constants. We solved that problem by adaptive stochastic optimization and describe our implementation of TMCMC sampling in the GNU MCSim software. Once a grid of perks is obtained, it is easy to perform posterior-tempered MCMC sampling or likelihood-tempered MCMC (thermodynamic integration, which bridges the joint prior and the posterior parameter distributions, with assured convergence of a single sampling chain). We compare TMCMC to other samplers and demonstrate its efficient sampling of multi-modal posteriors and calculation of Bayes factors in two stylized case-studies and two realistic population pharmacokinetic inference problems, one of them involving a large PBPK model.

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Data availability

Models’ code and simulation files are freely available from the official web page of GNU MCSim (www.gnu.org/software/mcsim).

Abbreviations

CV:

Coefficient of variation

MCMC:

Markov chain Monte Carlo

PBPK:

Physiologically-based pharmacokinetic

PK:

Pharmacokinetic

SD:

Standard deviation

TI:

Thermodynamic integration

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Acknowledgements

We thank Joost Beltman for helpful discussion of the results.

Funding

This study was supported in part by grant 1U01FD005838 from the U.S. Food and Drug Administration (FDA) and grant P42 ES027704 from the U.S. National Institutes of Health. This article reflects the views of the authors and should not be construed to represent FDA’s views or policies.

Author information

Authors and Affiliations

  1. Certara UK Limited, Simcyp Division, Sheffield, UK

    Frederic Y. Bois

  2. Department of Veterinary Integrative Biosciences, College of Veterinary Medicine and Biomedical Sciences, Texas A&M University, College Station, TX, USA

    Nan-Hung Hsieh & Weihsueh A. Chiu

  3. DRC/VIVA/METO Unit, INERIS, Verneuil en Halatte, France

    Wang Gao

  4. Department Chemical and Biological Engineering, School of Biomedical Engineering, Colorado State University, Fort Collins, CO, USA

    Brad Reisfeld

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  1. Frederic Y. Bois
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  2. Nan-Hung Hsieh
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  4. Weihsueh A. Chiu
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Contributions

FB, N-HH, WG, BR, and WC are listed as authors. FB conceived the overall research concept and design, had overall responsibility for its implementation, and performed most analyses, simulations, and their interpretation. N-HH and WC contributed to the theophylline and acetaminophen case studies. WG ran the Hamiltonian MCMC simulations. BR provided the original acetaminophen PBPK model and data. All authors reviewed the manuscript and revised it critically.

Corresponding author

Correspondence to Frederic Y. Bois.

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Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. FB is currently employed by the CERTARA company, but was not when this work was conducted.

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Bois, F.Y., Hsieh, NH., Gao, W. et al. Well-tempered MCMC simulations for population pharmacokinetic models. J Pharmacokinet Pharmacodyn 47, 543–559 (2020). https://doi.org/10.1007/s10928-020-09705-0

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