Generalized partial linear varying multi-index coefficient model for gene-environment interactions

Liu Xu, Gao Bin and Cui Yuehua ()
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Liu Xu: School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, China
Gao Bin: Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA
Cui Yuehua: Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA

Statistical Applications in Genetics and Molecular Biology, 2017, vol. 16, issue 1, 59-74

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.

Keywords: B-spline; backfitting; generalized likelihood ratio; kernel smoothing; single index model; varying coefficient model (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1515/sagmb-2016-0045

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