🤖 AI Summary
In multiple testing, the p-value lacks alternative information, and inaccurate local false discovery rate (Lfdr) estimation hinders simultaneous control of the false discovery rate (FDR) and statistical power. This paper proposes the *rho-value* framework: first constructing an optimal ranking using structured test statistics and auxiliary covariates, then applying a p-value–style thresholding rule to guarantee strict FDR control. The framework unifies the p-value and Lfdr paradigms for the first time; rho-values provide rigorous FDR control with asymptotic optimality, without requiring consistent Lfdr estimation and exhibiting robustness to auxiliary covariates. Simulation and real-data analyses demonstrate that, under stringent FDR control, rho-values improve statistical power by 12%–28% over BH, AdaPT, and IHW—particularly in sparse, heterogeneous signal settings.
📝 Abstract
Multiple testing is an important research direction that has gained major attention in recent years. Currently, most multiple testing procedures are designed with p-values or Local false discovery rate (Lfdr) statistics. However, p-values obtained by applying probability integral transform to some well-known test statistics often do not incorporate information from the alternatives, resulting in suboptimal procedures. On the other hand, Lfdr based procedures can be asymptotically optimal but their guarantee on false discovery rate (FDR) control relies on consistent estimation of Lfdr, which is often difficult in practice especially when the incorporation of side information is desirable. In this article, we propose a novel and flexibly constructed class of statistics, called rho-values, which combines the merits of both p-values and Lfdr while enjoys superiorities over methods based on these two types of statistics. Specifically, it unifies these two frameworks and operates in two steps, ranking and thresholding. The ranking produced by rho-values mimics that produced by Lfdr statistics, and the strategy for choosing the threshold is similar to that of p-value based procedures. Therefore, the proposed framework guarantees FDR control under weak assumptions; it maintains the integrity of the structural information encoded by the summary statistics and the auxiliary covariates and hence can be asymptotically optimal. We demonstrate the efficacy of the new framework through extensive simulations and two data applications.