Bayesian and frequentist methods and analyses of genome-wide association studies

Recent technological advances and remarkable successes have led to genome-wide association studies (GWAS) becoming a tool of choice for investigating the genetic basis of common complex human diseases. These studies typically involve samples from thousands of individuals, scanning their DNA at up to a million loci along the genome to discover genetic variants that affect disease risk. Hundreds of such variants are now known for common diseases, nearly all discovered by GWAS over the last three years. As a result, many new studies are planned for the future or are already underway. In this thesis, I present analysis results from actual studies and some developments in theory and methodology. The Wellcome Trust Case Control Consortium (WTCCC) published one of the first large-scale GWAS in 2007. I describe my contribution to this study and present the results from some of my follow-up analyses. I also present results from a GWAS of a bipolar disorder sub-phenotype, and a recent and on-going fine mapping experiment. Building on methods developed as part of the WTCCC, I describe a Bayesian approach to GWAS analysis and compare it to widely used frequentist approaches. I do so both theoretically, by interpreting each approach from the perspective of the other, and empirically, by comparing their performance in the context of replicated GWAS findings. I discuss the implications of these comparisons on the interpretation and analysis of GWAS generally, highlighting the advantages of the Bayesian approach. Finally, I examine the effect of linkage disequilibrium on the detection and estimation of various types of genetic effects, particularly non-additive effects. I derive a theoretical result showing how the power to detect a departure from an additive model at a marker locus decays faster than the power to detect an association