Admissibility in Partial Conjunction Testing

• 成果类型: Article
• 署名作者: Wang, Jingshu; Owen, Art B.
• 署名单位: University of Pennsylvania; Stanford University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2017.1385465
• 发表日期: 2019
• 页码: 158-168
• 关键词: metaanalysis; association; hypotheses; inference

摘要

Meta-analysis combines results from multiple studies aiming to increase power in finding their common effect. It would typically reject the null hypothesis of no effect if any one of the studies shows strong significance. The partial conjunction null hypothesis is rejected only when at least r of n component hypotheses are nonnull with r = 1 corresponding to a usual meta-analysis. Compared with meta-analysis, it can encourage replicable findings across studies. A by-product of it when applied to different r values is a confidence interval of r quantifying the proportion of nonnull studies. Benjamini and Heller (2008) provided a valid test for the partial conjunction null by ignoring the r - 1 smallest p-values and applying a valid meta-analysis p-value to the remaining n - r + 1 p-values. We provide sufficient and necessary conditions of admissible combined p-value for the partial conjunction hypothesis among monotone tests. Non-monotone tests always dominate monotone tests but are usually too unreasonable to be used in practice. Based on these findings, we propose a generalized form of Benjamini and Heller's test which allows usage of various types of meta-analysis p-values, and apply our method to an example in assessing replicable benefit of new anticoagulants across subgroups of patients for stroke prevention.