Efficient Prior Sensitivity and Tipping-point Analysis for Medical Research: Revisiting Sampling Importance Resampling

Abstract

Bayesian methods have received increasing attention in medical research, where sensitivity analysis of prior distributions is essential. Such analyses typically require the evaluation of the posterior distribution of a parameter under multiple alternative prior settings. When the posterior distribution of the parameter of interest cannot be derived analytically, the standard approach is to re-fit the model using Markov chain Monte Carlo (MCMC) for each setting, which incurs substantial computational costs. This issue is particularly relevant in tipping-point analysis, in which the posterior must be evaluated across gradually changing degrees of borrowing. Sampling-importance resampling (SIR) provides an efficient alternative by approximating posterior samples under new settings without MCMC re-fitting. Despite its potential computational advantages, the practical performance of SIR in repeated prior-sensitivity analyses, including tipping-point analysis, and in complex Bayesian models used in medical research has not been sufficiently illustrated. In this study, we illustrate the practical utility of SIR through two case studies: one involving tipping-point analysis under external data borrowing and another involving sensitivity analysis for a Bayesian nonparametric model in meta-analysis. In both examples, SIR substantially reduced computation time and produced posterior summaries similar to those obtained by MCMC re-fitting.