Discovering findings that replicate from a primary study of high dimension to a follow-up study

TL;DR

This paper develops new statistical methods to reliably identify findings that replicate across high-dimensional studies, addressing limitations of existing meta-analysis techniques and ensuring control over error rates.

Contribution

It introduces novel multiple testing procedures for replication analysis that control error rates under various dependence structures, improving reliability in high-dimensional research.

Findings

New procedures control FWER and FDR under dependence

Simulations and real data validate the methods' effectiveness

Methods outperform existing meta-analysis approaches

Abstract

We consider the problem of identifying whether findings replicate from one study of high dimension to another, when the primary study guides the selection of hypotheses to be examined in the follow-up study as well as when there is no division of roles into the primary and the follow-up study. We show that existing meta-analysis methods are not appropriate for this problem, and suggest novel methods instead. We prove that our multiple testing procedures control for appropriate error-rates. The suggested FWER controlling procedure is valid for arbitrary dependence among the test statistics within each study. A more powerful procedure is suggested for FDR control. We prove that this procedure controls the FDR if the test statistics are independent within the primary study, and independent or have dependence of type PRDS in the follow-up study. For arbitrary dependence within the primary study, and either arbitrary dependence or dependence of type PRDS in the follow-up study, simple conservative modifications of the procedure control the FDR. We demonstrate the usefulness of these procedures via simulations and real data examples.