High dimensional variable selection for gene-environment interactions

Abstract Gene-environment (G×E) interaction plays a pivotal role in understanding the genetic basis of complex disease. When environment factors are measured in a continuous scale, one can assess the genetic sensitivity over different environmental conditions on a disease phenotype. Motivated by the increasing awareness of the power of gene set based association analysis over single variant based approach, we proposed an additive varying-coefficient model to jointly model variants in a genetic system. The model allows us to examine how variants in a set are mediated by one or multiple environment factors to affect a disease phenotype. We approached the problem from a high dimensional variable selection perspective. In particular, we can select variants with varying, constant and zero coefficients, which correspond to cases of G×E interaction, no G×E interaction and no genetic effect, respectively. The procedure was implemented through a two stage iterative estimation algorithm via the Smoothly Clipped Absolute Deviation (SCAD) penalty function. Under certain regularity conditions, we established the consistency property in variable selection as well as effect separation of the two stage iterative estimators, and showed the optimal convergence rates of the estimates for varying effects. In addition, we showed that the estimate of non-zero constant coefficients enjoy the oracle property. The utility of our procedure was demonstrated through simulation studies and real data analysis.