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

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.

References in corpus (4)

• Multiple testing with discrete data: proportion of true null hypotheses and two adaptive FDR procedures
• False discovery rate control for multiple testing based on p-values with càdlàg distribution functions
• Multiple Test Functions and Adjusted p-Values for Test Statistics with Discrete Distributions
• On Benjamini-Hochberg procedure applied to mid p-values