Abstract
Identification of gene-environment (G × E) interactions associated with disease phenotypes has posed a great challenge in high-throughput cancer studies. The existing marginal identification methods have suffered from not being able to accommodate the joint effects of a large number of genetic variants, while some of the joint-effect methods have been limited by failing to respect the "main effects, interactions" hierarchy, by ignoring data contamination, and by using inefficient selection techniques under complex structural sparsity. In this article, we develop an effective penalization approach to identify important G × E interactions and main effects, which can account for the hierarchical structures of the 2 types of effects. Possible data contamination is accommodated by adopting the least absolute deviation loss function. The advantage of the proposed approach over the alternatives is convincingly demonstrated in both simulation and a case study on lung cancer prognosis with gene expression measurements and clinical covariates under the accelerated failure time model.