Title: Contributions to multivariate association models for nuclear families
Description: The etiology of a disease is based on a complex interplay of genetic and environmental factors. Utilizing information from the interaction of genes and the environment may elucidate genetic factors that would not be found otherwise. In chapters one and three we make novel contributions to family-based methodology for testing for gene-environment interaction. Additionally, determining the genetic components of a disease is complicated by the linkage disequilibrium, i.e. correlation, between genetic markers. In chapter two we make novel contributions to family-based methodology for determining whether one or more SNPs can explain the association of a genetic region with disease. In chapter one, we extend the FBAT-I gene-environment interaction test to utilize both trios and sibships. We then compare this extension to tests for the main effect of a gene, and joint tests of both the gene and gene-environment interaction. The methodology is applied to a group of nuclear families ascertained according to affection with Bipolar Disorder. In chapter two, we introduce methods to test for the effect of a set of markers conditional on another set of markers. We first propose a model-free extension of the FBAT main genetic effects test for quantitative and dichotomous traits. Then, for efficiency reasons, we introduce separate model-based tests for quantitative and dichotomous traits. The methodology is applied in a stepwise fashion to nuclear families in the Childhood Asthma Program in the IL10 gene.

In chapter three, we revisit gene-environment interaction tests. We extend the methods from the first chapter to a relative risk model that can be applied to any family structure. We then propose a more powerful approach using a logistic disease model that is applicable when there are discordant offspring. Lastly, we propose a hybrid of these approaches to utilize the more powerful approach whenever possible, while still gaining some information using the other approach when discordant offspring are not available. The methodology is applied to nuclear families affected with Chronic Obstructive Pulmonary Disease in the Serpine2 gene. All of the methodology proposed is implemented in the freely available fbati R package.