ZAP: $Z$-value Adaptive Procedures for False Discovery Rate Control with Side Information

TL;DR

This paper introduces ZAP, a novel covariate-adaptive method for FDR control that directly uses $z$-values instead of $p$-values, improving power and robustness in multiple testing scenarios with side information.

Contribution

It develops a $z$-value based adaptive testing procedure that guarantees FDR control under minimal assumptions and outperforms existing $p$-value based methods.

Findings

ZAP achieves higher power than traditional $p$-value methods.

FDR control is maintained even with model misspecification.

Performance improvements are demonstrated on simulated and real datasets.

Abstract

Adaptive multiple testing with covariates is an important research direction that has gained major attention in recent years. It has been widely recognized that leveraging side information provided by auxiliary covariates can improve the power of false discovery rate (FDR) procedures. Currently, most such procedures are devised with $p$-values as their main statistics. However, for two-sided hypotheses, the usual data processing step that transforms the primary statistics, known as $z$-values, into $p$-values not only leads to a loss of information carried by the main statistics, but can also undermine the ability of the covariates to assist with the FDR inference. We develop a $z$-value based covariate-adaptive (ZAP) methodology that operates on the intact structural information encoded jointly by the $z$-values and covariates. It seeks to emulate the oracle $z$-value procedure via a working model, and its rejection regions significantly depart from those of the $p$-value adaptive testing approaches. The key strength of ZAP is that the FDR control is guaranteed with minimal assumptions, even when the working model is misspecified. We demonstrate the state-of-the-art performance of ZAP using both simulated and real data, which shows that the efficiency gain can be substantial in comparison with $p$-value based methods. Our methodology is implemented in the $\texttt{R}$ package $\texttt{zap}$.