Xu, Zhiyuan2017-07-182017-07-182017-05https://hdl.handle.net/11299/188906University of Minnesota Ph.D. dissertation. May 2017. Major: Biostatistics. Advisor: Wei Pan. 1 computer file (PDF); ix, 101 pages.In spite of the huge success of the standard single-nucleotide polymorphism (SNP) based analysis in genome-wide association studies (GWASs), it has some limitations. First, it suffers power loss from a stringent significance level due to multiplicity adjust- ment for up to millions of tests. In addition, it has low power since the effect sizes of SNPs are usually small. Instead, gene-based testing might improve statistical power by aggregating moderate to weakly associated SNPs within each gene while greatly re- ducing the burden of multiple testing adjustment from millions to thousands. Second, almost all existing analyses do not explicitly account for (unknown) genetic hetero- geneity, leading to possible loss of power as convincingly shown in simulation studies (Londono et al., 2012; Qian and Shao, 2013; Zhou and Pan, 2009). Moreover, as there are many other data resources available (e.g. neuroimaging phenotypes, molecular phenotypes like gene expression) besides GWAS/DNA sequencing data, integrating them into GWAS is expected to boost statistical power. We first introduce a flexible framework to extend score-based testing in generalized linear models to more complex models, for example, mixed effect models. Second, we show that by accounting for genetic heterogeneity, more associated SNPs can be detected than the standard one-degree-of-freedom trend test in single SNP-based testing. Third, we propose a new adaptive aSPC test to detect associations between two random vectors in moderate to high dimensions; we also point out its connections to some existing association testing for multiple SNPs and multiple traits. Finally, we propose a novel gene-based association testing approach by incorporating weights derived from other data resources (e.g. from another eQTL dataset). We show the power gain of the new approach over two existing methods PrediXcan and TWAS, pointing out that both PrediXcan and TWAS are special cases of our new test.enaSPU testAssociation testingGWASImagingThesis or Dissertation