Robust semiparametric gene‐environment interaction analysis using sparse boosting

Abstract

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.

Gene–Environment Interaction: A Variable Selection Perspective

“…For example, Boosting, a popular machine learning method, aggregates multiple weak learners (individual features of weak predictive power for the response variable) into a strong learner (a model of strong predictive power) ( [54,55,56]). Within a regression framework, boosting has strong connections to penalization ( [57−59]), which makes it a natural choice for detecting important G × E interactions ( [60,61]). Support vector machine, another popular machine learning technique which is tightly connected to penalization in the form of "hinge loss + ridge penalty", can also be adopted for G × E interactions ( [62,63]).…”

“…Such a connection is the driving force of development of new boosting methods for detecting G × E interactions. As increasing amount of attention has been paid to robustness and hierarchical structure of interaction studies, Wu and Ma ( [61]) has proposed a robust semiparametric sparse Boosting approach for simultaneous identification of both linear and nonlinear interactions. They have adopted the Huber loss function for robustness, and a multiple imputation approach to accommodate missing values in the E factor.…”

“…Our summary in Section 2.1 shows that besides penalization and Bayesian methods, other popular machine learning methods have also been proposed. For example, the strategy of using a stagewise approach to progressively optimize the objective function has been adopted in Boosting based G × E studies ( [60,61]). 3.…”

Penalized Variable Selection for Lipid–Environment Interactions in a Longitudinal Lipidomics Study

“…Our model can be potentially extended in the following aspects. First, as data contamination and outliers have been widely observed in repeated measurements, robust variable selection methods in G × E interaction studies [23,[50][51][52] can be extended to longitudinal settings. Second, recently, multiple Bayesian methods have been proposed for pinpointing important G × E interaction effects [53][54][55].…”

Robust nonparametric integrative analysis to decipher heterogeneity and commonality across subgroups using sparse boosting

“…The proposed approach is based on sparse boosting, 19 which demonstrates competitive performances in high-dimensional data analysis compared to penalization and other techniques. 15,20 In all, this study is warranted by providing a practically useful new approach for exploring heterogeneity and commonality across multiple high-dimensional datasets.…”