This article introduces a sensitivity analysis method for Multiple Testing Procedures (MTPs) using marginal $p$-values. The method is based on the Dirichlet process (DP) prior distribution, specified to support the entire space of MTPs, where each MTP controls either the family-wise error rate (FWER) or the false discovery rate (FDR) under arbitrary dependence between $p$-values. The DP MTP sensitivity analysis method accounts for uncertainty in the selection of such MTPs and their respective cut-off points and decisions regarding which subset of $p$-values are significant from a given set of hypothesis tested, while measuring each $p$-value's probability of significance over the DP prior predictive distribution of this space of all MTPs, and reducing the possible conservativeness of using one such MTP for multiple testing. The DP MTP sensitivity analysis method is illustrated through the analysis of twenty-eight thousand $p$-values arising from hypothesis tests performed on a 2022 dataset of a representative sample of three million U.S. high school students observed on 239 variables. They include tests that relate variables about the disruption caused by school closures during the COVID-19 pandemic, with variables on mathematical cognition and academic achievement, and with student background variables. R software code for the DP MTP sensitivity analysis method is provided in the Appendix and in Supplementary Information.

翻译：本文提出了一种基于边缘$p$值的多重检验程序（MTP）敏感性分析方法。该方法以狄利克雷过程（DP）先验分布为基础，其设定覆盖了所有MTP的完整空间，其中每个MTP在$p$值存在任意依赖关系时均能控制族错误率（FWER）或错误发现率（FDR）。DP MTP敏感性分析方法综合考虑了以下因素的不确定性：MTP的选择、各检验的阈值截断点、以及从给定假设检验集合中判定哪些$p$值子集具有显著性。该方法通过计算每个$p$值在所有MTP空间的DP先验预测分布下的显著性概率，降低了在多重检验中仅使用单一MTP可能带来的保守性偏误。本文通过对2022年美国三百万高中生代表性样本的239个观测变量进行假设检验所产生的两万八千个$p$值进行分析，展示了DP MTP敏感性分析方法的实际应用。这些检验涉及以下变量间的关联分析：COVID-19疫情期间学校关闭造成的教育中断变量、数学认知与学业成就变量、以及学生背景变量。附录及补充信息中提供了DP MTP敏感性分析方法的R软件代码。