Title: Novel multivariate and Bayesian approaches to genetic association testing and integrated genomics
Description: At their best, genomewide association studies result in an increase in biological understanding of disease and lead to therapeutic targets. At their worst, these studies consume a large amount of funding only to publicize false positive results. The success of genomewide association scans depends on the availability of efficient and powerful statistical methods. In this thesis, I make a novel contribution to the body of statistical knowledge used to analyze these studies by fine-tuning existing methodology, applying an old method in a new context, and presenting an entirely new method for analyzing family-based studies. In chapter one, I compare the power of different ways to adjust standardized phenotypes. Standardized quantitative phenotypes such as percent of predicted forced expiratory volume and body mass index are used to measure underlying traits of interest (e.g., lung function, obesity). I recommend adjusting raw or standardized phenotypes within the study population via regression and illustrate through simulation and a data analysis that this results in optimal power in both population- and family-based association tests.

In the second chapter, we assess the potential of canonical correlation analysis for discovering regulatory variants. Our approach reduces multiple comparisons and may provide insight into the complex relationships between genotype and gene expression. Simulations suggest that canonical correlation analysis may have higher power to detect regulatory variants than pair-wise univariate regression when the expression trait has low heritability. The increase in power is even greater under the recessive model. In chapter three, I present a powerful Bayesian approach to family-based association testing. I construct a Bayes factor conditional on the offspring phenotype and parental genotype data and then use the data conditioned on to inform the prior odds for each marker. In constructing the prior odds, the evidence for association for each single marker is obtained at the population-level by estimating the genetic effect size in the conditional mean model. Since such genetic effect size estimates are statistically independent of the effect size estimation within the families, the actual data set can inform the construction of the prior odds without any statistical penalty.