In many statistical problems the hypotheses are naturally divided into groups, and the investigators are interested to perform group-level inference, possibly along with inference on individual hypotheses. We consider the goal of discovering groups containing $u$ or more signals with group-level false discovery rate (FDR) control. This goal can be addressed by multiple testing of partial conjunction hypotheses with a parameter $u,$ which reduce to global null hypotheses for $u=1.$ We consider the case where the partial conjunction $p$-values are combinations of within-group $p$-values, and obtain sufficient conditions on (1) the dependencies among the $p$-values within and across the groups, (2) the combining method for obtaining partial conjunction $p$-values, and (3) the multiple testing procedure, for obtaining FDR control on partial conjunction discoveries. We consider separately the dependencies encountered in the meta-analysis setting, where multiple features are tested in several independent studies, and the $p$-values within each study may be dependent. Based on the results for this setting, we generalize the procedure of Benjamini, Heller, and Yekutieli (2009) for assessing replicability of signals across studies, and extend their theoretical results regarding FDR control with respect to replicability claims.
翻译:在许多统计问题中,假设自然被分为若干组,调查人员有兴趣进行集团一级的推断,可能还想对个别假设进行推断。我们考虑的是发现含有美元或更多美元信号的团体与集团一级虚假发现率(FDR)控制的目标。这一目标可以通过对部分组合假设进行多次测试,并设定一个参数$u(美元),美元,该参数将美元减为全球无效假设,将美元减为1美元。我们认为,部分组合美元价值是集团内部价值的组合,并获得以下充分条件:(1) 美元价值在集团内部和集团之间的依赖关系;(2) 将获得部分组合美元价值的合并方法和(3) 多重测试程序结合起来,对部分组合发现进行FDR控制。我们分别考虑在元分析环境中遇到的相互依存关系,在几项独立研究中测试多种特征,每项研究中的美元价值可能取决于以下因素:(1) 依据这一结果,我们将部分组合美元价值在集团内部和集团之间具有依赖性;(2) 将部分组合美元价值的值与集团内部和集团之间具有依赖性;(2) 组合获得部分组合价值的美元价值的组合;(2) 获得部分组合美元价值的组合;(3) 对部分组合获得部分组合价值的美元价值的合并方法;(3) 和多重测试程序,以获得部分关联发现;我们普遍地评估关于Ben-Bell-Bell-Ral-Ral-C-C-R-R-R-R-C-R-R-S-S-C-R-R-R-R-R-R-R-R-R-C-S-S-S-S-R-R-R-R-R-R-C-R-R-R-C-C-C-R-R-R-R-C-R-R-R-R-R-R-C-R-R-R-C-C-R-R-R-R-C-R-R-C-C-C-C-C-C-C-C-C-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R-R