A Tournament Approach to Model Selection with Applications in Genome-wide Association Studies

Abstract

Recent genome-wide association studies in genetics pose many challenging problems for statisticians. One of such problems is model selection with a huge number of covariates. The data from genome-wide association studies typically consists of the measurement on a quantitative trait or a disease status (response variable) and the genotypes of a huge number of markers (covariates), say, tens or hundreds of thousands SNPs. The sample size however is relatively small. The currently existing methods for model selection are infeasible in this context. In this talk, we discuss a novel tournament approach to model selection. The approach consists of a stage-wise screening procedure, a permutation aggregating procedure, and a modified Bayesian model selection criterion. The stage-wise screening procedure assesses the joint covariate effects by using non-quadratic penalized likelihoods in stages, which mimics rounds of competitions in a tournament, hence gives rise to the name of the approach. The tournament approach is applied to a data set containing quantitative trait values and genotypes of 2155 SNPs of 16 pedigrees with 233 individuals. It is demonstrated by simulation studies that the tournament approach is powerful in detecting multiple associations and at the same time incurs low false discovery rate.