IDEAS home Printed from https://ideas.repec.org/a/bpj/sagmbi/v17y2018i2p18n1.html

Additive varying-coefficient model for nonlinear gene-environment interactions

Author

Listed:
  • Wu Cen

    (Department of Statistics, Kansas State University, Manhattan, KS 66506, USA)

  • Zhong Ping-Shou

    (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)

Abstract

Gene-environment (G×E) interaction plays a pivotal role in understanding the genetic basis of complex disease. When environmental factors are measured continuously, one can assess the genetic sensitivity over different environmental conditions on a disease trait. Motivated by the increasing awareness of gene set based association analysis over single variant based approaches, we proposed an additive varying-coefficient model to jointly model variants in a genetic system. The model allows us to examine how variants in a gene set are moderated by an environment factor to affect a disease phenotype. We approached the problem from a variable selection perspective. In particular, we select variants with varying, constant and zero coefficients, which correspond to cases of G×E interaction, no G×E interaction and no genetic effect, respectively. The procedure was implemented through a two-stage iterative estimation algorithm via the smoothly clipped absolute deviation penalty function. Under certain regularity conditions, we established the consistency property in variable selection as well as effect separation of the two stage iterative estimators, and showed the optimal convergence rates of the estimates for varying effects. In addition, we showed that the estimate of non-zero constant coefficients enjoy the oracle property. The utility of our procedure was demonstrated through simulation studies and real data analysis.

Suggested Citation

  • Wu Cen & Zhong Ping-Shou & Cui Yuehua, 2018. "Additive varying-coefficient model for nonlinear gene-environment interactions," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 17(2), pages 1-18, April.
    • Handle: RePEc:bpj:sagmbi:v:17:y:2018:i:2:p:18:n:1
    DOI: 10.1515/sagmb-2017-0008
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/sagmb-2017-0008
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/sagmb-2017-0008?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Zhang, Hao Helen & Cheng, Guang & Liu, Yufeng, 2011. "Linear or Nonlinear? Automatic Structure Discovery for Partially Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1099-1112.
    2. Arnab Maity & Raymond J. Carroll & Enno Mammen & Nilanjan Chatterjee, 2009. "Testing in semiparametric models with interaction, with applications to gene–environment interactions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 75-96, January.
    3. Nilanjan Chatterjee & Raymond J. Carroll, 2005. "Semiparametric maximum likelihood estimation exploiting gene-environment independence in case-control studies," Biometrika, Biometrika Trust, vol. 92(2), pages 399-418, June.
    4. Yi-Hau Chen & Nilanjan Chatterjee & Raymond J. Carroll, 2013. "Using shared genetic controls in studies of gene-environment interactions," Biometrika, Biometrika Trust, vol. 100(2), pages 319-338.
    5. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    6. A. Antoniadis & I. Gijbels & S. Lambert-Lacroix, 2014. "Penalized estimation in additive varying coefficient models using grouped regularization," Statistical Papers, Springer, vol. 55(3), pages 727-750, August.
    7. Jianhua Z. Huang, 2002. "Varying-coefficient models and basis function approximations for the analysis of repeated measurements," Biometrika, Biometrika Trust, vol. 89(1), pages 111-128, March.
    8. Wang, Lifeng & Li, Hongzhe & Huang, Jianhua Z., 2008. "Variable Selection in Nonparametric Varying-Coefficient Models for Analysis of Repeated Measurements," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1556-1569.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Feng, Sanying & He, Wenqi & Li, Feng, 2020. "Model detection and estimation for varying coefficient panel data models with fixed effects," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    2. Hu Yang & Chaohui Guo & Jing Lv, 2016. "Variable selection for generalized varying coefficient models with longitudinal data," Statistical Papers, Springer, vol. 57(1), pages 115-132, March.
    3. Jun Yan & Jian Huang, 2012. "Model Selection for Cox Models with Time-Varying Coefficients," Biometrics, The International Biometric Society, vol. 68(2), pages 419-428, June.
    4. Zhao, Weihua & Jiang, Xuejun & Lian, Heng, 2018. "A principal varying-coefficient model for quantile regression: Joint variable selection and dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 269-280.
    5. Heng Lian & Peng Lai & Hua Liang, 2013. "Partially Linear Structure Selection in Cox Models with Varying Coefficients," Biometrics, The International Biometric Society, vol. 69(2), pages 348-357, June.
    6. A. Antoniadis & I. Gijbels & S. Lambert-Lacroix, 2014. "Penalized estimation in additive varying coefficient models using grouped regularization," Statistical Papers, Springer, vol. 55(3), pages 727-750, August.
    7. Qu, Lianqiang & Song, Xinyuan & Sun, Liuquan, 2018. "Identification of local sparsity and variable selection for varying coefficient additive hazards models," Computational Statistics & Data Analysis, Elsevier, vol. 125(C), pages 119-135.
    8. Lian, Heng & Li, Jianbo & Tang, Xingyu, 2014. "SCAD-penalized regression in additive partially linear proportional hazards models with an ultra-high-dimensional linear part," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 50-64.
    9. Zhang, Shen & Zhao, Peixin & Li, Gaorong & Xu, Wangli, 2019. "Nonparametric independence screening for ultra-high dimensional generalized varying coefficient models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 37-52.
    10. Kangning Wang & Lu Lin, 2019. "Robust and efficient estimator for simultaneous model structure identification and variable selection in generalized partial linear varying coefficient models with longitudinal data," Statistical Papers, Springer, vol. 60(5), pages 1649-1676, October.
    11. Aleksey Kolokolov & Shifan Yu, 2026. "Realized Regularized Regressions," Papers 2604.23023, arXiv.org.
    12. Lian, Heng, 2015. "Quantile regression for dynamic partially linear varying coefficient time series models," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 49-66.
    13. Li Liu & Hao Wang & Yanyan Liu & Jian Huang, 2021. "Model pursuit and variable selection in the additive accelerated failure time model," Statistical Papers, Springer, vol. 62(6), pages 2627-2659, December.
    14. Chaohui Guo & Hu Yang & Jing Lv, 2017. "Robust variable selection in high-dimensional varying coefficient models based on weighted composite quantile regression," Statistical Papers, Springer, vol. 58(4), pages 1009-1033, December.
    15. Zhang, Ting, 2015. "Semiparametric model building for regression models with time-varying parameters," Journal of Econometrics, Elsevier, vol. 187(1), pages 189-200.
    16. Byeong U. Park & Enno Mammen & Young K. Lee & Eun Ryung Lee, 2015. "Varying Coefficient Regression Models: A Review and New Developments," International Statistical Review, International Statistical Institute, vol. 83(1), pages 36-64, April.
    17. Heng Lian & Xin Chen & Jian-Yi Yang, 2012. "Identification of Partially Linear Structure in Additive Models with an Application to Gene Expression Prediction from Sequences," Biometrics, The International Biometric Society, vol. 68(2), pages 437-445, June.
    18. Jun Jin & Tiefeng Ma & Jiajia Dai, 2021. "New efficient spline estimation for varying-coefficient models with two-step knot number selection," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(5), pages 693-712, July.
    19. Rui Li & Chenlei Leng & Jinhong You, 2017. "A Semiparametric Regression Model for Longitudinal Data with Non-stationary Errors," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(4), pages 932-950, December.
    20. Rahul Ghosal & Arnab Maity & Timothy Clark & Stefano B. Longo, 2020. "Variable selection in functional linear concurrent regression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(3), pages 565-587, June.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bpj:sagmbi:v:17:y:2018:i:2:p:18:n:1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.degruyterbrill.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.