Semiparametric nonlinear regression for detecting gene and environment interactions

Abstract It is commonly accepted that gene and environment (G × E) interactions play a pivotal role in determining the risk of human diseases. In conventional parametric models such as linear models and generalized linear models which are applied frequently to study statistical interactions, effects of covariates are decomposed into main effects and interaction effects (products of two components). Such decomposition, however, may not reflect the true interaction effect of gene and environment. In this paper, we propose a semiparametric regression approach to capture possible nonlinear G × E interactions. A profile quasi-log-likelihood estimation method is applied with asymptotic consistency and normality established for the profile estimators. Moreover, we develop Rao-score-type test procedures based on the profile estimation for regression parameters and nonparametric coefficient functions, respectively. Our models and methods are illustrated by both simulation studies and analysis of a dataset application.

[1]  Avshalom Caspi,et al.  Gene–environment interactions in psychiatry: joining forces with neuroscience , 2006, Nature Reviews Neuroscience.

[2]  J. Hebebrand,et al.  Environmental and genetic risk factors in obesity. , 2009, Child and adolescent psychiatric clinics of North America.

[3]  Nilanjan Chatterjee,et al.  Semiparametric maximum likelihood estimation exploiting gene-environment independence in case-control studies , 2005 .

[4]  Liugen Xue,et al.  Statistical inference for a single-index varying-coefficient model , 2013, Stat. Comput..

[5]  Xiaotong Shen,et al.  Local asymptotics for regression splines and confidence regions , 1998 .

[6]  T. Dawber,et al.  Epidemiological approaches to heart disease: the Framingham Study. , 1951, American journal of public health and the nation's health.

[7]  Raymond J Carroll,et al.  Semiparametric Bayesian analysis of gene-environment interactions with error in measurement of environmental covariates and missing genetic data. , 2011, Statistics and its interface.

[8]  Testing for Constant Nonparametric Effects in General Semiparametric Regression Models with Interactions. , 2011, Statistics & probability letters.

[9]  W. Härdle,et al.  Semi-parametric estimation of partially linear single-index models , 2006 .

[10]  Yuehua Cui,et al.  Varying coefficient model for gene-environment interaction: a non-linear look , 2011, Bioinform..

[11]  R. W. Wedderburn.  Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method , 1974 .

[12]  Niels Grarup,et al.  Gene–environment interactions in the pathogenesis of type 2 diabetes and metabolism , 2007, Current opinion in clinical nutrition and metabolic care.

[13]  Jinbo Chen,et al.  Semiparametric Maximum Likelihood Methods for Analyzing Genetic and Environmental Effects with Case‐Control Mother–Child Pair Data , 2012, Biometrics.

[14]  J. Cheverud,et al.  A simple correction for multiple comparisons in interval mapping genome scans , 2001, Heredity.

[15]  D. Kang,et al.  Breast cancer prevention based on gene–environment interaction , 2011, Molecular Carcinogenesis.

[16]  Wolfgang Härdle,et al.  Partially Linear Models , 2000 .

[17]  Jaeil Ahn,et al.  BAYESIAN SEMIPARAMETRIC ANALYSIS FOR TWO-PHASE STUDIES OF GENE-ENVIRONMENT INTERACTION. , 2013, The annals of applied statistics.

[18]  Arnab Maity,et al.  Testing in semiparametric models with interaction, with applications to gene-environment interactions. , 2009, Journal of the Royal Statistical Society. Series B, Statistical methodology.

[19]  Jianqing Fan,et al.  Generalized Partially Linear Single-Index Models , 1997 .

[20]  Ulf Ekelund,et al.  Physical activity and obesity prevention: a review of the current evidence , 2005, Proceedings of the Nutrition Society.

[21]  Liugen Xue,et al.  Empirical likelihood for single-index varying-coefficient models , 2012 .

[22]  K. Knutson.  Does inadequate sleep play a role in vulnerability to obesity? , 2012, American journal of human biology : the official journal of the Human Biology Council.

[23]  D. Nyholt.  A simple correction for multiple testing for single-nucleotide polymorphisms in linkage disequilibrium with each other. , 2004, American journal of human genetics.

[24]  C. Cockerham,et al.  An Extension of the Concept of Partitioning Hereditary Variance for Analysis of Covariances among Relatives When Epistasis Is Present. , 1954, Genetics.

[25]  Philippa J Talmud,et al.  Gene-environment interaction and its impact on coronary heart disease risk. , 2007, Nutrition, metabolism, and cardiovascular diseases : NMCD.

[26]  Jianqing Fan,et al.  Efficient Estimation and Inferences for Varying-Coefficient Models , 2000 .

[27]  Runze Li,et al.  ESTIMATION AND TESTING FOR PARTIALLY LINEAR SINGLE-INDEX MODELS. , 2010, Annals of statistics.

[28]  S. Faraone,et al.  Gene-environment interactions in mental disorders. , 2004, World psychiatry : official journal of the World Psychiatric Association.