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Incorporating the number of true null hypotheses to improve power in multiple testing: application to gene microarray data

Testing for significance with gene expression data from DNA microarray experiments involves simultaneous comparisons of hundreds or thousands of genes. In common exploratory microarray experiments, most genes are not expected to be differentially expressed. The family-wise error (FWE) rate and false discovery rate (FDR) are two common approaches used to account for multiple hypothesis tests to identify differentially expressed genes. When the number of hypotheses is very large and some null hypotheses are expected to be true, the power of an FWE or FDR procedure can be improved if the number of null hypotheses is known. The mean of differences (MD) of ranked p-values has been proposed to estimate the number of true null hypotheses under the independence model. This article proposes to incorporate the MD estimate into an FWE or FDR approach for gene identification. Simulation results show that the procedure appears to control the FWE and FDR well at the FWE=0.05 and FDR=0.05 significant levels; it exceeds the nominal level for FDR=0.01 when the null hypotheses are highly correlated, a correlation of 0.941. The proposed approach is applied to a public colon tumor data set for illustration.