Set-Based Tests for the Gene–Environment Interaction in Longitudinal Studies

We propose a generalized score type test for set-based inference for the gene–environment interaction with longitudinally measured quantitative traits. The test is robust to misspecification of within subject correlation structure and has enhanced power compared to existing alternatives. Unlike tests for marginal genetic association, set-based tests for the gene–environment interaction face the challenges of a potentially misspecified and high-dimensional main effect model under the null hypothesis. We show that our proposed test is robust to main effect misspecification of environmental exposure and genetic factors under the gene–environment independence condition. When genetic and environmental factors are dependent, the method of sieves is further proposed to eliminate potential bias due to a misspecified main effect of a continuous environmental exposure. A weighted principal component analysis approach is developed to perform dimension reduction when the number of genetic variants in the set is large relative to the sample size. The methods are motivated by an example from the Multi-Ethnic Study of Atherosclerosis (MESA), investigating interaction between measures of neighborhood environment and genetic regions on longitudinal measures of blood pressure over a study period of about seven years with four exams. Supplementary materials for this article are available online.