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

ABSTRACT

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.

KEYWORDS:

• Gene–environment independence
• Generalized score test
• MESA neighborhood study
• Model misspecification
• Robustness

Supplemental Materials

We present the detailed proofs, additional numerical studies, and additional data analysis of MESA in the supplementary materials. The supplementary materials includes 7 figures and 12 tables.

Funding

This work was supported by NSF DMS 1406712 and NIH/NIEHS grant ES020811, NIH/NHLBI grant R00HL113164, NIH/NHLBI HL101161, and NIMHHD Grant 2P60MD002249 Center for Integrative Approaches to health Disparities (CIAHD). MESA and the MESA SHARe project are conducted and supported by the National Heart, Lung, and BloodInstitute (NHLBI) in collaboration with MESA investigators. Support for MESA is provided by contracts N01-HC-95159, N01-HC-95160, N01-HC-95161, N01-HC-95162, N01-HC-95163, N01-HC-95164, N01-HC-95165, N01-HC-95166,N01-HC-95167, N01-HC-95168, N01-HC-95169 and CTSAUL1-RR-024156. Funding for SHARe genotyping was provided by NHLBI Contract N02-HL-64278. Genotyping was performed at Affymetrix (Santa Clara, California, USA) and the Broad Institute of Harvard and MIT (Boston, MA, USA) using the Affymetrix Genome-Wide HumanSNP Array 6.0.