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

Author

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  • Liu Xu

    (School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, China)

  • Gao Bin
  • Cui Yuehua

    (Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA)

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.

Suggested Citation

  • Liu Xu & Gao Bin & Cui Yuehua, 2017. "Generalized partial linear varying multi-index coefficient model for gene-environment interactions," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 16(1), pages 59-74, March.
    • Handle: RePEc:bpj:sagmbi:v:16:y:2017:i:1:p:59-74:n:6
    DOI: 10.1515/sagmb-2016-0045
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    References listed on IDEAS

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    1. Li, Yehua & Wang, Naisyin & Carroll, Raymond J., 2010. "Generalized Functional Linear Models With Semiparametric Single-Index Interactions," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 621-633.
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    3. Paul Zimmet & K. G. M. M. Alberti & Jonathan Shaw, 2001. "Global and societal implications of the diabetes epidemic," Nature, Nature, vol. 414(6865), pages 782-787, December.
    4. Fan, Jianqing & Jiang, Jiancheng, 2005. "Nonparametric Inferences for Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 890-907, September.
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