Abstract
The false discovery proportion (FDP), the proportion of incorrect rejections among all rejections, is a direct measure of abundance of false positive findings in multiple testing. Many methods have been proposed to control FDP, but they are too conservative to be useful for power analysis. Study designs for controlling the mean of FDP, which is false discovery rate, have been commonly used. However, there has been little attempt to design study with direct FDP control to achieve certain level of efficiency. We provide a sample size calculation method using the variance formula of the FDP under weak-dependence assumptions to achieve the desired overall power. The relationship between design parameters and sample size is explored. The adequacy of the procedure is assessed by simulation. We illustrate the method using estimated correlations from a prostate cancer dataset.
Highlights
Modern biomedical research frequently involves parallel measurements of a large number of quantities of interest, such as gene expression levels, single nucleotide polymorphism SNP and DNA copy number variations
We provide a more general method of sample size calculation for controlling FDP under weak-dependence assumptions
Under the assumptions of common effect size and weak dependence among test statistics, explicit formulas for the mean μQ and variance σQ2 of the FDP have been derived 23 : μQ ≈ π0α π0α
Summary
Modern biomedical research frequently involves parallel measurements of a large number of quantities of interest, such as gene expression levels, single nucleotide polymorphism SNP and DNA copy number variations. This is a more stringent criterion than FDR because the proportion of false rejections is bounded above by r1 with high probability. When we design studies involving multiple testing, it is important to determine sample size to ensure adequate statistical power. Methods for calculating sample size have been proposed to control various criteria, for example, FWER 12–14 , FDR 15–20 , the number of false discoveries 19, 21 and FDP 22. For controlling FDP, Oura et al 22 provided a method to calculate sample size using the beta-binomial model for the sum of rejection status of true alternative hypotheses. We provide a more general method of sample size calculation for controlling FDP under weak-dependence assumptions. We illustrate the sample size calculation procedure using a prostate cancer dataset
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