A General Study of Genetic Association Tests and the Test of Hardy-Weinberg Equilibrium

A great number of statistical methods have been developed to test genetic association between a heritable trait and a genetic marker. However, no single existing method can deal with multiple analytical challenges that include, for example, evaluating multiple (binary and continuous) traits simultaneously, being robust to departure from Hardy-Weinberg equilibrium (HWE), and analyzing correlated data from pedigrees. Further, there is much confusion about the analytical differences and similarities between the different association tests. This thesis work fills in this gap by developing a new analytical framework, which also unifies some of the existing methods for simple yet commonly seen settings. Chapter 1 provides the scientific motivation and genetic background. Chapter 2 focuses on genotype- based approaches, introduces a new ‘reverse’ or retrospective regression model that tests association in related samples with adjustment to Hardy-Weinberg disequilibrium (HWD), and shows the theoretical link between the proposed genotype-based test and the existing ones. Chapters 3 and 4 expand the genotype-based retrospective regression to a robust allele-based (RA) alternative, and generalize the locally most powerful allelic association test to accommodate complex data scenarios. Chapter 5 takes a fresh look at the role of HWD in association analysis, and proposes a RA joint test that leverages the HWD attributed to true association to increase testing power yet remains robust to HWD attributed to genotyping error. Finally, Chapter 6 revisits all the tests introduced in the earlier chapters, and provides additional insights on the analytical connections between the prospective and retrospective regression frameworks, between regression-based and non-parametric methods, and between genotype-based and allele-based association tests.Ph.D