Statistical Methods for Marker Discovery and Disease Risk Prediction Amid Unobserved Genetic Interactions

Many human traits, including Mendelian disorders, are now recognized to have complex genetic architecture, and demand innovative statistical approaches to identify the contributing genetic factors. Genetic interaction effects are widely believed to play an important role in the pathophysiology of such complex traits; however, many of these interactions remain undiscovered due to a lack of knowledge or collection of the relevant exposures, or feasibility in examining enormous numbers of interaction combinations. In this thesis, I explore two important consequences to statistical analysis amid unobserved genetic interactions. (1) Artificially induced variance heterogeneity across genotype groups for quantitative traits and (2) increased prediction bias at the extremes of risk for survival models. For both cases, I develop statistical methodology to address the corresponding limitations. For (1), I propose a joint location-scale testing (JLS) framework that simultaneously tests the null hypothesis of equal mean and equal variance between genotype groups, by aggregating association evidence from the individual location-only and scale-only tests, focusing on Fishers method of combining information (JLS-Fisher). I also extend Levene's test for variance heterogeneity and the JLS framework to analyze more complex data structures involving genotype/group uncertainty and dependent observations. For (2), I propose a new calibration test for Cox models that leverages additional power from biased risk estimates at the tails of risk distribution. The test aggregates martingale residuals for subjects from extreme high and low risk groups with a test statistic maximum chosen by varying which risk groups are included in the extremes. The methods developed in this thesis are evaluated alongside existing approaches through simulation studies. Data sets involving patients with cystic fibrosis and patients with type 1 diabetes are used to demonstrate that additional power can be gained from methods that account for potential missing interactions over conventional methods.Ph.D