Adjustment for Multiplicity

The number of comparisons of gene expression level studied in a microarray experiment has been growing literarily at an exponential rate since the beginning of the 1990s. Considering a microarray data analyzed by testing each gene, multiple testing is an immediate concern. When many hypotheses are tested, the probability that a type I error is committed increases sharply with the number of hypotheses. This problem of multiplicity is not unique to microarray technology, yet its magnitude here, where a single experiment may involve many thousands of genes, dramatically intensifies the problem.In this chapter, we discuss a few procedures controlling for the FWER, such as the Bonferroni, Holm, and the maxT procedures. However, the focus of this chapter is controlling the FDR criterion, since it admits a more powerful outcome. We discuss several variations of the Benjamini and Hochberg step-up procedure (BH-FDR 1995), the permutation-based FDR controlling procedures, and the significance analysis of microarrays (SAM) approach of Tusher et al. (Proc Natl Acad Sci 98:5116–5121, 2001) and the Efron et al. (J Am Stat Assoc 96:1151–1160, 2001), and Storey (A direct approach to false discovery rates. Technical Report. Stanford University, Stanford, 2001) Bayesian interpretation of the FDR within the context of microarray data.