While there have been extensive statistical methods on gene-environment interaction (GEI) in case-control studies, little attention has been given to robust and efficient modeling of GEI in longitudinal cohort studies. In a two-way table for GEI with row and column as categorical variables, a conventional saturated model involves estimation of distinct interaction effect for each cell. However, the degrees of freedom (df) for testing interaction can grow quickly with increasing number of categories, resulting in decreased efficiency and reduced power for detecting interaction. This dissertation considers the problem of modeling GEI with repeated measures data on a quantitative trait using parsimonious models for non-additivity proposed in the classical Analysis of Variance literature. We first provide an overview of these classical models and explore the interaction structures by simply reducing repeated measurements to summary level cell means. In the first project, we modify the cell-mean method and propose a parametric bootstrap approach using these interaction models. Both methods account for the unbalanced and longitudinal nature of the data. In the second project, we propose a shrinkage estimator that combines estimates from a saturated interaction model and Tukey;;s single df model for non-additivity. It is useful for conducting multiple GEI tests where distinct interaction patterns could occur in different genetic markers. The proposed estimator is robust to various interaction structures and the corresponding test is valid based on simulation results. In the third project, we focus on additive main effects and multiplicative interaction (AMMI) models. We develop an alternating maximum likelihood estimation procedure for AMMI models and approximate the null distribution of the likelihood ratio test statistic by a chi-square with fractional df. The proposed methods are illustrated using data from the Normative Aging Study and the Multi-Ethnic Study of Atherosclerosis. Both datasets come from longitudinal cohort studies involving rich genetic data and several environmental exposure factors that could be time varying or time invariant. Overall, this dissertation contributes to adaptation of classical interaction models to longitudinal studies, with the goal of understanding the dynamic interplay between genes and environment over time.
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Robust and Efficient Modeling for Gene-Environment and Gene-Gene Interactions in Longitudinal Cohort Studies.