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Title: Comparing several adaptive multiple testing methods for discrete uniform homogeneous $p$-values Authors:  Marta Cousido Rocha - University of Vigo (Spain) [presenting]
Jacobo de Una-Alvarez - University of Vigo (Spain)
Sebastian Doehler - Darmstadt University of Applied Science (Germany)
Abstract: Large-scale discrete uniform homogeneous $p$-values arise in many applications, for example, in genome wide association studies. Several multiple testing procedures for such $p$-values are compared through simulations. Specifically, we consider the $q$-value approach based on several estimators for the proportion of true null hypotheses $\pi_0$: the usual estimator for continuous and possibly heterogeneous $p$-values, and two estimators proposed recently for discrete $p$-values. One of these two proposals is focused on discrete uniform homogeneous $p$-values while we adapt the other one, originally valid for discrete heterogeneous $p$-values to uniform $p$-values. The simulated scenario is that of the two-sample problem with low sample size, along a large number of locations or genes. The considered test statistics are the standard student's $t$ test, a permutation test based on the absolute deviation between the sample means, the Kolmogorov-Smirnov two-sample test, and a permutation test based on the $L_2$ distance between the empirical characteristic functions pertaining to the two samples. The main conclusion is that the specific estimator for $\pi_0$ influences the power a lot, and that the approaches for discrete $p$-values may or may not improve the $q$-value procedure based on the continuous estimator of $\pi_0$.