Improved $q$-values for discrete uniform and homogeneous tests: a comparative study

TL;DR

This paper compares various methods for calculating q-values in discrete uniform and homogeneous tests, focusing on their theoretical properties, performance in simulations, and applications to genetic and financial data.

Contribution

It provides a comprehensive review and comparison of existing estimators for π₀ in discrete settings, including practical recommendations.

Findings

Discrete q-values improve false discovery rate control in discrete tests.

Performance varies depending on the estimator of π₀ used.

Simulations and real data applications demonstrate the methods' effectiveness.

Abstract

Large scale discrete uniform and homogeneous $P$-values often arise in applications with multiple testing. For example, this occurs in genome wide association studies whenever a nonparametric one-sample (or two-sample) test is applied throughout the gene loci. In this paper we consider $q$-values for such scenarios based on several existing estimators for the proportion of true null hypothesis, $\pi_0$, which take the discreteness of the $P$-values into account. The theoretical guarantees of the several approaches with respect to the estimation of $\pi_0$ and the false discovery rate control are reviewed. The performance of the discrete $q$-values is investigated through intensive Monte Carlo simulations, including location, scale and omnibus nonparametric tests, and possibly dependent $P$-values. The methods are applied to genetic and financial data for illustration purposes too. Since the particular estimator of $\pi_0$ used to compute the $q$-values may influence the power, relative advantages and disadvantages of the reviewed procedures are discussed. Practical recommendations are given.