Multiple comparison procedures for discrete uniform and homogeneous tests

Abstract

Discrete uniform and homogeneous p-values often arise in applications with multiple testing. For example, this occurs in genome wide association studies whenever a non-parametric one-sample (or two-sample) test is applied throughout the gene loci. In this paper, we consider multiple comparison procedures for such scenarios based on several existing estimators for the proportion of true null hypotheses, p0, which take the discreteness of the p-values into account. The theoretical guarantees of the several approaches with respect to the estimation of p0 and the false discovery rate control are reviewed. The performance of the discrete procedures is investigated through intensive Monte Carlo simulations considering both independent and dependent p-values. The methods are applied to three real data sets for illustration purposes too. Since the particular estimator of p0 used to compute the q-values may influence its performance, relative advantages and disadvantages of the reviewed procedures are discussed. Practical recommendations are given.