Robust semiparametric gene-environment interaction analysis using sparse boosting.

For the pathogenesis of complex diseases, gene-environment (G-E) interactions have been shown to have important implications. G-E interaction analysis can be challenging with the need to jointly analyze a large number of main effects and interactions and to respect the "main effects, interactions" hierarchical constraint. Extensive methodological developments on G-E interaction analysis have been conducted in recent literature. Despite considerable successes, most of the existing studies are still limited as they cannot accommodate long-tailed distributions/data contamination, make the restricted assumption of linear effects, and cannot effectively accommodate missingness in E variables. To directly tackle these problems, a semiparametric model is assumed to accommodate nonlinear effects, and the Huber loss function and Qn estimator are adopted to accommodate long-tailed distributions/data contamination. A regression-based multiple imputation approach is developed to accommodate missingness in E variables. For model estimation and selection of relevant variables, we adopt an effective sparse boosting approach. The proposed approach is practically well motivated, has intuitive formulations, and can be effectively realized. In extensive simulations, it significantly outperforms multiple direct competitors. The analysis of The Cancer Genome Atlas data on stomach adenocarcinoma and cutaneous melanoma shows that the proposed approach makes sensible discoveries with satisfactory prediction and stability.