Admissibility in Partial Conjunction Testing
Abstract
Metaanalysis 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 metaanalysis. Compared with metaanalysis, it can encourage replicable findings across studies. A byproduct 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 pvalues and applying a valid metaanalysis pvalue to the remaining $n  r + 1$ pvalues. We provide sufficient and necessary conditions of admissible combined pvalue for the partial conjunction hypothesis among monotone tests. Nonmonotone 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 metaanalysis pvalues, and apply our method to an example in assessing replicable benefit of new anticoagulants across subgroups of patients for stroke prevention.
 Publication:

arXiv eprints
 Pub Date:
 August 2015
 arXiv:
 arXiv:1508.00934
 Bibcode:
 2015arXiv150800934W
 Keywords:

 Mathematics  Statistics Theory;
 Statistics  Methodology