title: Generalized partial linear varying multi-index coefficient model for gene-environment interactions.
abstract: Epidemiological studies have suggested the joint effect of simultaneous exposures to multiple environments on disease risk. However, how environmental mixtures as a whole jointly modify genetic effect on disease risk is still largely unknown. Given the importance of gene-environment (G×E) interactions on many complex diseases, rigorously assessing the interaction effect between genes and environmental mixtures as a whole could shed novel insights into the etiology of complex diseases. For this purpose, we propose a generalized partial linear varying multi-index coefficient model (GPLVMICM) to capture the genetic effect on disease risk modulated by multiple environments as a whole. GPLVMICM is semiparametric in nature which allows different index loading parameters in different index functions. We estimate the parametric parameters by a profile procedure, and the nonparametric index functions by a B-spline backfitted kernel method. Under some regularity conditions, the proposed parametric and nonparametric estimators are shown to be consistent and asymptotically normal. We propose a generalized likelihood ratio (GLR) test to rigorously assess the linearity of the interaction effect between multiple environments and a gene, while apply a parametric likelihood test to detect linear G×E interaction effect. The finite sample performance of the proposed method is examined through simulation studies and is further illustrated through a real data analysis.
authors.forename: Xu
authors.initials: X
authors.lastname: Liu
authors.forename: Bin
authors.initials: B
authors.lastname: Gao
authors.forename: Yuehua
authors.initials: Y
authors.lastname: Cui
mesh_terms: D003198:Computer Simulation; D004194:Disease; D059647:Gene-Environment Interaction; D006801:Humans; D016014:Linear Models; D008954:Models, Biological; D012306:Risk