Modified FDR controlling procedure for multi-stage analyses

Multiple testing has become an integral component in genomic analyses involving microarray experiments where a large number of hypotheses are tested simultaneously. However, before applying more computationally intensive methods, it is often desirable to complete an initial truncation of the variable set using a simpler and faster supervised method such as univariate regression. Once such a truncation is completed, multiple testing methods applied to any subsequent analysis no longer control the appropriate Type I error rates. Here we propose a modified marginal Benjamini & Hochberg step-up FDR controlling procedure for multi-stage analyses (FDR-MSA), which correctly controls Type I error in terms of the entire variable set when only a subset of the initial set of variables is tested. The method is presented with respect to a variable importance application. As the initial subset size increases, we observe convergence to the standard Benjamini & Hochberg step-up FDR controlling multiple testing procedures. We demonstrate the power and Type I error control through simulation and application to the Golub Leukemia data from 1999.