Testing partial conjunction hypotheses under dependency, with applications to meta-analysis

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)102-155
Number of pages54
JournalElectronic Journal of Statistics
Volume17
Issue number1
DOIs
StatePublished - 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

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