Resampling-based multiple testing for microarray data analysis
The burgeoning field of genomics has revived interest in multiple testing procedures by raising new methodological and computational challenges. For example, microarray experiments generate large multiplicity problems in which thousands of hypotheses are tested simultaneously. In their 1993 book, Westfall & Young propose resampling-based $p$-value adjustment procedures which are highly relevant to microarray experiments. This article discusses different criteria for error control in resampling-based multiple testing, including (a) the family wise error rate of Westfall & Young's 1993 book and (b) the false discovery rate developed by Benjamini & Hochberg's 1995 paper, both from a frequentist viewpoint; and (c) the positive false discovery rate of Storey's 2002 paper published in J.R.S.S.B, which has a Bayesian motivation. We also introduce our recently developed fast algorithm for implementing the minP adjustment to control family-wise error rate. Adjusted $p$-values for different approaches are applied to gene expression data from two recently published microarray studies. The properties of these procedures for multiple testing are compared.