Ray, Debashree2017-10-092017-10-092015-07https://hdl.handle.net/11299/190503University of Minnesota Ph.D. dissertation. July 2015. Major: Biostatistics. Advisor: Saonli Basu. 1 computer file (PDF); ix, 139 pages.Most common human diseases are complex genetic traits, with multiple genetic and environmental components contributing to the disease susceptibility. Genome-wide Association Studies (GWASs) offer a powerful approach to identify the genetic variants (single nucleotide polymorphisms or SNPs) that modulate the susceptibility to these complex diseases. GWASs have identified hundreds of SNPs associated with such diseases, but these SNPs appear to explain very little of the genetic risk. This dissertation aims at investigating several alternative hypotheses for explaining the disease risk and develop statistical techniques to improve the power to detect SNPs influencing such diseases. A Bayesian dimension reduction model is developed to study the joint effect of a group of SNPs on the disease status for unrelated individuals. Modeling the joint effects of multiple SNPs can help in the detection of SNPs that jointly have significant risk effects but individually make only a small contribution. Thus, our method based on the proposed dimension reduction model, Bayesian partitioning model (BPM), may have improved power over multiple single-SNP association analysis when testing the association of multiple SNPs with a single binary trait. Similarly, joint analysis of multiple disease-related traits may also improve detection of SNPs associated with a disease. GWASs often collect data on multiple disease-related traits. These traits may share a common set of SNPs influencing them and a joint analysis of these traits may improve the power to detect these SNPs which may provide a better understanding of the underlying disease mechanism. Multivariate analysis of variance (MANOVA) can perform such an association analysis at a GWAS level. The behavior of MANOVA is investigated, both theoretically and using simulations, and the conditions where MANOVA loses power are derived. Based on these findings, a novel unified score-based association test (USAT) is proposed that adaptively uses the data to optimize power to detect association of a single SNP with multiple quantitative phenotypes/traits. This test and other such multivariate tests are based on the assumption of random sampling, and may suffer from severely inflated type I error in case of selected sampling. This motivated us to explore scenarios in which popular methods would fail to provide valid tests of the null hypothesis of no association of a single SNP with multiple traits within the framework of a case-control study. Two alternative hypothesis testing approaches (one based on maximum p-value and the other based on propensity score) are proposed for such scenarios.enAssociation StudyBayesian dimension reductionCase-control StudyMultiple PhenotypesMultivariate analysisSecondary phenotypesThesis or Dissertation