title: Varying coefficient model for gene-environment interaction: a non-linear look.
abstract: BACKGROUND
  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.
  
  
  RESULTS
  In this work, we propose to relax the linear G×E 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 help us to gain novel insights into the etiology of a complex disease. Several statistical tests are proposed for 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 and testable framework for assessing non-linear G×E interaction.
authors.affiliation: Department of Statistics and Probability, Michigan State University, East Lansing, Michigan 48824, USA.
authors.forename: Shujie
authors.initials: S
authors.lastname: Ma
authors.forename: Lijian
authors.initials: L
authors.lastname: Yang
authors.forename: Roberto
authors.initials: R
authors.lastname: Romero
authors.forename: Yuehua
authors.initials: Y
authors.lastname: Cui
mesh_terms: D019295:Computational Biology / Q000379:methods*; D003198:Computer Simulation; D004777:Environment; D020022:Genetic Predisposition to Disease; D006801:Humans; D007231:Infant, Newborn; D008957:Models, Genetic; D015233:Models, Statistical; D009010:Monte Carlo Method; D017711:Nonlinear Dynamics; D019683:Penetrance; D010641:Phenotype; D020641:Polymorphism, Single Nucleotide