Use of spurious correlation for multiplicity adjustment

TL;DR

This paper introduces a novel approach to multiple testing that uses spurious correlation estimates to enhance statistical power while asymptotically controlling the family-wise error rate, demonstrated through simulations and real data.

Contribution

It proposes using non-consistent, spurious correlation estimates for multiplicity adjustment to improve power in multiple testing scenarios.

Findings

Proposed method asymptotically controls family-wise error rate.

Method provides higher statistical power than existing approaches.

Validated through simulations and real data application.

Abstract

We consider one of the most basic multiple testing problems that compares expectations of multivariate data among several groups. As a test statistic, a conventional (approximate) $t$-statistic is considered, and we determine its rejection region using a common rejection limit. When there are unknown correlations among test statistics, the multiplicity adjusted $p$-values are dependent on the unknown correlations. They are usually replaced with their estimates that are always consistent under any hypothesis. In this paper, we propose the use of estimates, which are not necessarily consistent and are referred to as spurious correlations, in order to improve statistical power. Through simulation studies, we verify that the proposed method asymptotically controls the family-wise error rate and clearly provides higher statistical power than existing methods. In addition, the proposed and existing methods are applied to a real multiple testing problem that compares quantitative traits among groups of mice and the results are compared.