Varying coefficient model for geneenvironment interaction: a non-linear look

The genetic basis of a complex trait often involves the function of multiple genetic factors, their interactions and the interaction between the genetic and environmental factors. Geneenvironment (G×E) interaction is considered pivotal in determining trait variations and susceptibility of many genetic disorders such as neurodegenerative diseases or mental disorders. Regressionbased method assuming a linear relationship between a disease response and the genetic and environmental factors as well as their interaction is the commonly used approach in detecting G×E interaction. The linearity assumption, however, could be easily violated due to the nonlinear interaction between the genetic and environment factors. In this work, we propose to relax the linearity assumption and allow for non-linear G×E interaction under a varying coefficient model framework. We propose to estimate the varying coefficients with regression spline technique. The model allows one to assess the non-linear penetrance of a genetic variant under different environmental stimuli, therefore could help us to gain novel insights into the etiology of a complex disease. Various hypothesis tests are proposed toward a complete dissection of G×E interaction. A wild bootstrap method is adopted to assess the statistical significance. Both simulation and real data analysis demonstrate the power and utility of the proposed method. Our method provides a powerful alternative and a testable framework for assessing non-linear G×E interaction. 1 Varying coefficient model for G×E interaction 1