Multiple testing has become an integral component in genomic analyses involving microarray experiments where 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 procedure. We demonstrate the power and Type I error control through simulation and application to the Golub Leukemia data from 1999.
Statistical Methodology | Statistical Theory
Tuglus, Catherine and van der Laan, Mark J., "FDR Controlling Procedure for Multi-stage Analyses" (July 2008). U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 239.