Flexible and efficient Bayesian pharmacometrics modeling using Stan and Torsten, Part I

A novel Bayesian generative approach for estimating tumor dynamics from published studies

Tumor growth inhibition (TGI) modeling attempts to describe the time course changes in tumor size for patients undergoing cancer therapy. TGI models present several advantages over traditional exposure-response models that are based explicitly on clinical end points and have become a popular tool in the pharmacometrics community. Unfortunately, the data required to fit TGI models, namely longitudinal tumor measurements, are sparse or often not available in literature or publicly accessible databases. On the contrary, common end points such as progression-free survival (PFS) and objective response rate (ORR) are directly derived from longitudinal tumor measurements and are routinely published. To this end, a Bayesian generative model relating underlying tumor dynamics to summary PFS and ORR data is introduced to learn TGI model parameters using only published summary data. The parameterized model can describe the tumor dynamics, quantify treatment effect, and account for differences in the study population. The utility of this model is shown by applying it to several published studies, and learned parameters are combined to simulate an in silico trial of a novel combination therapy in a novel setting.

Bayesian estimation in veterinary pharmacology: A conceptual and practical introduction

Sophisticated mathematical and computational tools have become widespread and important in veterinary pharmacology. Although the theoretical basis and practical applications of these have been widely explored in the literature, statistical inference in the context of these models has received less attention. Optimization methods, often with frequentist statistical inference, have been predominant. In contrast, Bayesian statistics have not been widely applied, but offer both practical utility and arguably greater interpretability. Veterinary pharmacology applications are generally well supported by relevant prior information, from either existing substantive knowledge, or an understanding of study and model design. This facilitates practical implementation of Bayesian analyses that can take advantage of this knowledge. This essay will explore the specification of Bayesian models relevant to veterinary pharmacology, including demonstration of prior selection, and illustrate the capability of these models to generate practically useful statistics, including uncertainty statements, that are difficult or impossible to obtain otherwise. Case studies using simulated data will describe applications in clinical trials, pharmacodynamics, and pharmacokinetics, all including multilevel modeling. This content may serve as a suitable starting point for researchers in veterinary pharmacology and related disciplines considering Bayesian estimation for their applied work.

Bayesian Calibration to Address the Challenge of Antimicrobial Resistance: A Review

Antimicrobial resistance (AMR) emerges when disease-causing microorganisms develop the ability to withstand the effects of antimicrobial therapy. This phenomenon is often fueled by the human-to-human transmission of pathogens and the overuse of antibiotics. Over the past 50 years, increased computational power has facilitated the application of Bayesian inference algorithms. In this comprehensive review, the basic theory of Markov Chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC) methods are explained. These inference algorithms are instrumental in calibrating complex statistical models to the vast amounts of AMR-related data. Popular statistical models include hierarchical and mixture models as well as discrete and stochastic epidemiological compartmental and agent based models. Studies encompassed multi-drug resistance, economic implications of vaccines, and modeling AMR in vitro as well as within specific populations. We describe how combining these topics in a coherent framework can result in an effective antimicrobial stewardship. We also outline recent advancements in the methodology of Bayesian inference algorithms and provide insights into their prospective applicability for modeling AMR in the future.

Bayesian inference for fitting cardiac models to experiments: estimating parameter distributions using Hamiltonian Monte Carlo and approximate Bayesian computation

Customization of cardiac action potential models has become increasingly important with the recognition of patient-specific models and virtual patient cohorts as valuable predictive tools. Nevertheless, developing customized models by fitting parameters to data poses technical and methodological challenges: despite noise and variability associated with real-world datasets, traditional optimization methods produce a single "best-fit" set of parameter values. Bayesian estimation methods seek distributions of parameter values given the data by obtaining samples from the target distribution, but in practice widely known Bayesian algorithms like Markov chain Monte Carlo tend to be computationally inefficient and scale poorly with the dimensionality of parameter space. In this paper, we consider two computationally efficient Bayesian approaches: the Hamiltonian Monte Carlo (HMC) algorithm and the approximate Bayesian computation sequential Monte Carlo (ABC-SMC) algorithm. We find that both methods successfully identify distributions of model parameters for two cardiac action potential models using model-derived synthetic data and an experimental dataset from a zebrafish heart. Although both methods appear to converge to the same distribution family and are computationally efficient, HMC generally finds narrower marginal distributions, while ABC-SMC is less sensitive to the algorithmic settings including the prior distribution.