Multiple Comparison Procedures

Abstract

In the previous chapter, several traditional statistical methods were described for testing for an association between a genotype and a trait. These methods generally require comparing a test statistic to its known (or simulated) distribution in order to quantify the probability of seeing what we do or something more extreme under the assumption that the null hypothesis is true. Our decision to accept or reject the null then rests on a comparison of this quantity, called the p-value, to a threshold based on a previously determined acceptable level of error. In population-based association studies, we generally aim to test for the presence of associations between the trait and each of multiple genotypes across several SNPs and gene loci. As we saw in Section 2.3 and describe in more detail below, testing multiple hypotheses can result in an ination of the error rate, which we want to control. Several methods, termed simulta- neous test procedures (STPs), have been developed to address this challenge directly. In this chapter, a few such methods for adjusting for multiple testing are described, including single-step and step-down methods (Section 4.2) and resampling-based approaches (Section 4.3). First, some important measures of error are defined (Section 4.1). The advanced reader is referred to the more theoretical coverage of multiple testing procedures and their latest developments in Dudoit and van der Laan (2008), Dudoit et al. (2003) and Chapter 16 of Gentleman et al. (2005). These discussions include applications to data arising from gene expression studies, human genetic association studies and HIV genetic investigations.