Abstract
In many statistical problems the hypotheses are naturally di-vided 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 pro-cedure, for obtaining FDR control on partial conjunction discoveries. We consider separately the dependencies encountered in the meta-analysis set-ting, 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 Yeku-tieli (2009) for assessing replicability of signals across studies, and extend their theoretical results regarding FDR control with respect to replicability claims.
Original language | English |
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Pages (from-to) | 102-155 |
Number of pages | 54 |
Journal | Electronic Journal of Statistics |
Volume | 17 |
Issue number | 1 |
DOIs | |
State | Published - 2023 |
Keywords
- False discovery rate
- global null
- meta-analysis
- partial conjunction hypothesis
- replicability analysis
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty