Heterocedasticity-Adjusted Ranking and Thresholding for Large-Scale Multiple Testing

TL;DR

This paper introduces HART, a heteroscedasticity-adjusted ranking and thresholding method for large-scale multiple testing that directly uses variances, leading to higher power and better FDR control than standardization-based methods.

Contribution

The paper proposes a novel heteroscedasticity-adjusted testing procedure that exploits variance information to improve power in multiple testing scenarios.

Findings

HART outperforms existing methods in power at the same FDR level.

HART is asymptotically valid and optimal for FDR control.

Simulation and real data demonstrate HART's effectiveness.

Abstract

Standardization has been a widely adopted practice in multiple testing, for it takes into account the variability in sampling and makes the test statistics comparable across different study units. However, despite conventional wisdom to the contrary, we show that there can be a significant loss in information from basing hypothesis tests on standardized statistics rather than the full data. We develop a new class of heteroscedasticity--adjusted ranking and thresholding (HART) rules that aim to improve existing methods by simultaneously exploiting commonalities and adjusting heterogeneities among the study units. The main idea of HART is to bypass standardization by directly incorporating both the summary statistic and its variance into the testing procedure. A key message is that the variance structure of the alternative distribution, which is subsumed under standardized statistics, is highly informative and can be exploited to achieve higher power. The proposed HART procedure is shown to be asymptotically valid and optimal for false discovery rate (FDR) control. Our simulation results demonstrate that HART achieves substantial power gain over existing methods at the same FDR level. We illustrate the implementation through a microarray analysis of myeloma.