A two-step multiple comparison procedure for a large number of tests and multiple treatments

For situations where the number of tested hypotheses is increasingly large, the power to detect statistically significant multiple treatment effects decreases. As is the case with microarray technology, often researchers are interested in identifying differentially expressed genes for more than two types of cells or treatments. A two-step procedure is proposed for the purpose of increasing power to detect significant effects (i.e., to identify differentially expressed genes). Specifically, in the first step, the null hypothesis of equality across the mean expression levels for all treatments is tested for each gene. In the second step, only pairwise comparisons corresponding to the genes for which the treatment means are statistically different in the first step are tested. We propose an approach to estimate the overall FDR for both fixed rejection regions and fixed FDR significance levels. Also proposed is a procedure to find the FDR significance levels used in the first step and the second step such that the overall FDR can be controlled below a pre-specified FDR significance level. When compared via simulation the two-step approach has increased power over a one-step procedure, and controls the FDR at a desire significance level.