Statistical Methodologies for Genetic Association Studies with Rare Variants

In the search for genetic factors that are associated with complex heritable human traits, considerable attention has been focussed on rare variants that individually have small effects. Many recent papers have proposed testing strategies to detect association between traits and groups of rare variants with competing claims about the performance of various tests. The power of a given test in fact depends on the nature of any association and on the rareness of the variants in question.In this thesis we review such tests within a unified framework that covers a whole range of genetic models. We divide tests into linear and quadratic classes. We study performance of both classes through exact and asymptotic power calculations and novel simulation studies. We show that test statistics from both classes are complementary and they are powerful under limited settings. To achieve robustness, we propose to combine the evidence of association from two or more complementary tests. We consider the minimum-p and Fisher's methods of combining p-values from linear and quadratic statistics. Our extensive simulation studies show that both methods are robust across wide range of genetic models and have comparable or better power than alternative methods such as weighted kernel-based association tests. Our results also show that power to detect association in plausible genetic scenarios is low for studies of medium size unless a high proportion of the chosen variants are causal. To increase power, we also consider response-dependent sampling in association studies with rare variants. We also show that, under a broad range of generalized likelihoods and sampling plans, score statistic for testing association between a response Y and genetic variants are identical for two main likelihood approaches, and are of the same form as for ordinary random sampling on Y. Lastly, we evaluate proposed methodology and various sampling strategies with extensive simulations.Ph.D