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

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, 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 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 π0 used to compute the q-values may influence the power, relative advantages and disadvantages of the reviewed procedures are discussed. Practical recommendations are given.