Integrative analysis of gene-environment interactions under a multi-response partially linear varying coefficient model

Consider the integrative analysis of genetic data with multiple correlated response variables. The goal is to identify important gene-environment (G × E) interactions along with main gene and environment effects that are associated with the responses. The homogeneity and heterogeneity models can be adopted to describe the genetic basis of multiple responses. To accommodate possible nonlinear effects of some environment effects, a multi-response partially linear varying coefficient model is assumed. Penalization is adopted for marker selection. The proposed penalization method can select genetic variants with G × E interactions, no G × E interactions, and no main effects simultaneously. It adopts different penalties to accommodate the homogeneity and heterogeneity models. The proposed method can be effectively computed using a coordinate descent algorithm. Simulation study and the analysis of Health Professionals Follow-up Study, which has two correlated continuous traits, SNP measurements and multiple environment effects, show superior performance of the proposed method over its competitors.