Hierarchical selection of genetic and gene by environment interaction effects in high-dimensional mixed models

Interactions between genes and environmental factors may play a key role in the etiology of many common disorders. Several regularized generalized linear models (GLMs) have been proposed for hierarchical selection of gene by environment interaction (GEI) effects, where a GEI effect is selected only if the corresponding genetic main effect is also selected in the model. However, none of these methods allow to include random effects to account for population structure, subject relatedness and shared environmental exposure. In this paper, we develop a unified approach based on regularized penalized quasi-likelihood (PQL) estimation to perform hierarchical selection of GEI effects in sparse regularized mixed models. We compare the selection and prediction accuracy of our proposed model with existing methods through simulations under the presence of population structure and shared environmental exposure. We show that for all simulation scenarios, compared to other penalized methods, our proposed method enforced sparsity by controlling the number of false positives in the model while having the best predictive performance. Finally, we apply our method to a real data application using the Orofacial Pain: Prospective Evaluation and Risk Assessment (OPPERA) study, and found that our method retrieves previously reported significant loci.