Designing a GWAS: power, sample size, and data structure.

In this chapter we describe a novel Bayesian approach to designing GWAS studies with the goal of ensuring robust detection of effects of genomic loci associated with trait variation.The goal of GWAS is to detect loci associated with variation in traits of interest. Finding which of 500,000-1,000,000 loci has a practically significant effect is a difficult statistical problem, like finding a needle in a haystack. We address this problem by designing experiments to detect effects with a given Bayes factor, where the Bayes factor is chosen sufficiently large to overcome the low prior odds for genomic associations. Methods are given for various possible data structures including random population samples, case-control designs, transmission disequilibrium tests, sib-based transmission disequilibrium tests, and other family-based designs including designs for plants with clonal replication. We also consider the problem of eliciting prior information from experts, which is necessary to quantify prior odds for loci. We advocate a "subjective" Bayesian approach, where the prior distribution is considered as a mathematical representation of our prior knowledge, while also giving generic formulae that allow conservative computations based on low prior information, e.g., equivalent to the information in a single sample point. Examples using R and the R packages ldDesign are given throughout.