Bayesian Methods for Calibrating Health Policy Models: A Tutorial

Nicolas A. Menzies, Djøra I. Soeteman, Ankur Pandya, Jane J. Kim

Mathematical simulation models are commonly used to inform health policy decisions. These health policy models represent the social and biological mechanisms that determine health and economic outcomes, combine multiple sources of evidence about how policy alternatives will impact those outcomes, and synthesize outcomes into summary measures salient for the policy decision. Calibrating these health policy models to fit empirical data can provide face validity and improve the quality of model predictions. Bayesian methods provide powerful tools for model calibration. These methods summarize information relevant to a particular policy decision into (1) prior distributions for model parameters, (2) structural assumptions of the model, and (3) a likelihood function created from the calibration data, combining these different sources of evidence via Bayes' theorem. This article provides a tutorial on Bayesian approaches for model calibration, describing the theoretical basis for Bayesian calibration approaches as well as pragmatic considerations that arise in the tasks of creating calibration targets, estimating the posterior distribution, and obtaining results to inform the policy decision. These considerations, as well as the specific steps for implementing the calibration, are described in the context of an extended worked example about the policy choice to provide (or not provide) treatment for a hypothetical infectious disease. Given the many simplifications and subjective decisions required to create prior distributions, model structure, and likelihood, calibration should be considered an exercise in creating a reasonable model that produces valid evidence for policy, rather than as a technique for identifying a unique theoretically optimal summary of the evidence.