Semiparametric nonlinear regression for detecting gene and environment interactions

•Proposed a new semiparametric model for nonlinear gene and environment interactions.•Showed that effects of genetic factors can be altered by environmental factors.•Developed a profile quasi-log-likelihood estimation method.•Developed Rao-score-type tests for parameters and coefficient functions.

It is commonly accepted that gene and environment (G××E) interactions play a pivotal role in determining the risk of human diseases. In conventional parametric models such as linear models and generalized linear models which are applied frequently to study statistical interactions, effects of covariates are decomposed into main effects and interaction effects (products of two components). Such decomposition, however, may not reflect the true interaction effect of gene and environment. In this paper, we propose a semiparametric regression approach to capture possible nonlinear G××E interactions. A profile quasi-log-likelihood estimation method is applied with asymptotic consistency and normality established for the profile estimators. Moreover, we develop Rao-score-type test procedures based on the profile estimation for regression parameters and nonparametric coefficient functions, respectively. Our models and methods are illustrated by both simulation studies and analysis of a dataset application.