On estimating the proportion of true null hypotheses for false discovery rate controlling procedures in exploratory DNA microarray studies

Multiple testing using DNA microarray gene expression data has revived the promising area of false discovery rate (FDR) in statistics. Some recent advances in FDR controlling procedures can be unified in terms of estimating the proportion of true null hypotheses, π₀. In the original FDR procedure π₀ was set to its upper bound of one, the most conservative choice. The degree of conservativeness in estimating π₀ has a direct impact on the power of FDR procedures to detect true alternative hypotheses. In this work, we examine some recent FDR procedures with respect to the following two primary aims: (1) Compare the conservativeness of estimating π₀ (and hence FDR). (2) Evaluate the impact of (1) on the power to detect true alternative hypotheses. We also investigate the sensitivity of FDR procedures to violation of statistical assumptions, such as heterogeneity of variance and independence. The effect of varying sample sizes on the estimation of π₀ and power is also explored. Furthermore, in our investigation of aims (1) and (2), we defined and utilized the benchmark FDR procedure. This allows for making absolute power comparisons of FDR procedures to a benchmark, in addition to making relative comparisons among FDR procedures.