A Practitioner's Guide to Bayesian Inference in Pharmacometrics using Pumas

This paper provides a comprehensive tutorial for Bayesian practitioners in pharmacometrics using Pumas workflows. We start by giving a brief motivation of Bayesian inference for pharmacometrics highlighting limitations in existing software that Pumas addresses. We then follow by a description of all the steps of a standard Bayesian workflow for pharmacometrics using code snippets and examples. This includes: model definition, prior selection, sampling from the posterior, prior and posterior simulations and predictions, counter-factual simulations and predictions, convergence diagnostics, visual predictive checks, and finally model comparison with cross-validation. Finally, the background and intuition behind many advanced concepts in Bayesian statistics are explained in simple language. This includes many important ideas and precautions that users need to keep in mind when performing Bayesian analysis. Many of the algorithms, codes, and ideas presented in this paper are highly applicable to clinical research and statistical learning at large but we chose to focus our discussions on pharmacometrics in this paper to have a narrower scope in mind and given the nature of Pumas as a software primarily for pharmacometricians.