  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.
