Coombes, Brandon2016-12-192016-12-192016-08https://hdl.handle.net/11299/183388University of Minnesota Ph.D. dissertation. August 2016. Major: Biostatistics. Advisor: Saonli Basu. 1 computer file (PDF); ix, 98 pages.Complex diseases are caused by a combination of environmental and genetic factors. While we have estimated that genetic factors explain a large proportion of variance in many of these diseases, current strategies using only the genotyped common variants (CVs) have failed to explain all of this heritability. There are many hypotheses for this so-called “missing heritability.” We study two such hypotheses by extending a sequential algorithm that was initially proposed to test for genetic main effects of a candidate gene. We first extend the model selection test using the sequential algorithm to a model-averaging test. We use these tests to study how rare variants (RVs) rather than CVs may explain a larger proportion of the disease risk and apply our methods to a candidate gene study of obesity that has sequenced CVs and RVs. It is also thought that the effect of the variants is moderated by environmental fac- tors. Thus, gene-environment interactions may explain why we are not able to identify genes that cause disease. To improve power to detect gene-environment interactions for variants within a candidate gene in studies with unrelated or related subjects, we extend the sequential algorithm for the model selection test for genetic main effects to instead test for these interactions. For studies with unrelated subjects, we extend the sequential algorithm to create summary measures for either the genetic main effect or the interaction and show that these tests are often valid under realistic scenarios. We use a combination of the main effect and interaction summary measures to powerfully test for gene-environment interaction in a variety of situations. We apply our method to test whether candidate genes interact with family climate to influence alcohol consumption among a parent population. Lastly, we extend the tests of gene-environment interaction for unrelated subjects to families. We model the family data using a linear mixed model (LMM) framework to account for shared genetic and environmental effects within a family. In order to reduce the number of parameters we need to estimate, we propose using a ridge penalty on the genetic main effect re-expressed as a random effect within the LMM. We also develop a test which is weighted version of a previous test using the sum of powers of the score vector for interaction where weights are chosen with our sequential algorithm. We show that this test can be more powerful than the previous test when there are a mix of positive and negative interaction effects. We apply our test to a twin study to identify significant interactions between the CVs of candidate genes and a set of environmental factors that influence alcohol consumption.enDimension reductionFamilyGene-environment interactionModel-averagingRare variantsScore testThesis or Dissertation