The genetic basis of complex traits often involves the function of multiple genetic factors, their interactions and the interaction between the genetic and environmental factors. Gene-environment (G×E) interaction is considered pivotal in determining trait variations and susceptibility of many genetic disorders such as neurodegenerative diseases or mental disorders. Regression-based methods 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 non-linear genetic penetrance which induces non-linear G×E interaction.