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arXiv · 2006.01882

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

Marta Cousido-Rocha·Jacobo de Uña-Álvarez·Sebastian Döhler
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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.

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Marta Cousido-Rocha, Jacobo de Uña-Álvarez, Sebastian Döhler. 2020-06-02. Improved $q$-values for discrete uniform and homogeneous tests: a comparative study. https://doi.org/10.1111/rssc.12529

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