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 Markov chain Monte Carlo (MCMC) algorithm 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. However, to our knowledge , its utility has not been evaluated in scenarios involving repeated MCMC -- such as tipping-point analysis -- or in the application of complex Bayesian models. In this study, we re-evaluate the utility of SIR through two case studies: one involving tipping-point analysis under external data borrowing and another involving sensitivity analysis for a nonparametric Bayesian model in meta-analysis. These examples demonstrate that SIR can significantly reduce computational costs while maintaining a reasonable approximation accuracy.

翻译：贝叶斯方法在医学研究中日益受到关注，其中先验分布的敏感性分析至关重要。此类分析通常需要评估参数在多种替代先验设置下的后验分布。当目标参数的后验分布无法解析推导时，标准方法是为每种设置重新拟合马尔可夫链蒙特卡洛（MCMC）算法，这会带来巨大的计算成本。该问题在转折点分析中尤为突出，此类分析需要在逐渐变化的借用程度下评估后验分布。抽样重要性重抽样（SIR）提供了一种高效替代方案，可在无需重新拟合MCMC的情况下近似获得新设置下的后验样本。然而，据我们所知，其效用尚未在涉及重复MCMC（如转折点分析）的场景或复杂贝叶斯模型的应用中得到评估。本研究通过两个案例重新评估SIR的效用：一个涉及外部数据借用下的转折点分析，另一个涉及荟萃分析中非参数贝叶斯模型的敏感性分析。这些案例表明，SIR能在保持合理近似精度的同时显著降低计算成本。