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, π0, which take the discreteness of the p‐values into account. The theoretical guarantees of the several approaches with respect to the estimation of π0 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 π0 used to compute the q‐values may influence its performance, relative advantages and disadvantages of the reviewed procedures are discussed. Practical recommendations are given.

TwoSampleTest.HD: An R Package for the Two-Sample Problem with High-Dimensional Data

“…However, these results should be taken with some caution since exact KS p-values could not be computed by ks.test function due to the presence of ties in Hedenfalk data; note that the asymptotic distribution of the KS test may be inaccurate for small sample sizes. The lack of power of KS in the multiple testing setting has been pointed out in Cousido-Rocha et al (2021) too. Similarly as for KS, Levene test does not declare any gene as differently expressed in the two tumor groups; this is not surprising, since differences between the two groups are mainly due to a location shift (Hedenfalk et al, 2001).…”