Prospective calculation of identification power for individual genes in analyses controlling the false discovery rate

Recent work on prospective power and sample size calculations for analyses of high-dimension gene expression data that control the false discovery rate (FDR) focuses on the average power over all the truly nonnull hypotheses, or equivalently, the expected proportion of nonnull hypotheses rejected. Using another characterization of power, we adapt Efron's ([2007] Ann Stat 35:1351-1377) empirical Bayes approach to post hoc power calculation to develop a method for prospective calculation of the "identification power" for individual genes. This is the probability that a gene with a given true degree of association with clinical outcome or state will be included in a set within which the FDR is controlled at a specified level. An example calculation using proportional hazards regression highlights the effects of large numbers of genes with little or no association on the identification power for individual genes with substantial association.