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Partially linear single index Cox regression model in nested case-control studies

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Listed:
  • Shang, Shulian
  • Liu, Mengling
  • Zeleniuch-Jacquotte, Anne
  • Clendenen, Tess V.
  • Krogh, Vittorio
  • Hallmans, Goran
  • Lu, Wenbin

Abstract

The nested case-control (NCC) design is widely used in epidemiologic studies as a cost-effective subcohort sampling method to study the association between a disease and its potential risk factors. NCC data are commonly analyzed using Thomas’ partial likelihood approach under the Cox proportional hazards model assumption. However, the linear modeling form in the Cox model may be insufficient for practical applications, especially when there are a large number of risk factors under investigation. In this paper, we consider a partially linear single index proportional hazards model, which includes a linear component for covariates of interest to yield easily interpretable results and a nonparametric single index component to adjust for multiple confounders effectively. We propose to approximate the nonparametric single index function by polynomial splines and estimate the parameters of interest using an iterative algorithm based on the partial likelihood. Asymptotic properties of the resulting estimators are established. The proposed methods are evaluated using simulations and applied to an NCC study of ovarian cancer.

Suggested Citation

  • Shang, Shulian & Liu, Mengling & Zeleniuch-Jacquotte, Anne & Clendenen, Tess V. & Krogh, Vittorio & Hallmans, Goran & Lu, Wenbin, 2013. "Partially linear single index Cox regression model in nested case-control studies," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 199-212.
    • Handle: RePEc:eee:csdana:v:67:y:2013:i:c:p:199-212
    DOI: 10.1016/j.csda.2013.05.011
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    References listed on IDEAS

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    1. Yu Y. & Ruppert D., 2002. "Penalized Spline Estimation for Partially Linear Single-Index Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1042-1054, December.
    2. Jeng‐Min Chiou & Hans‐Georg Müller, 2004. "Quasi‐Likelihood Regression with Multiple Indices and Smooth Link and Variance Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(3), pages 367-386, September.
    3. Yingcun Xia & Howell Tong & W. K. Li & Li‐Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410, August.
    4. Xiangrong Yin & R. Dennis Cook, 2002. "Dimension reduction for the conditional kth moment in regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 159-175, May.
    5. Stoker, Thomas M, 1986. "Consistent Estimation of Scaled Coefficients," Econometrica, Econometric Society, vol. 54(6), pages 1461-1481, November.
    6. Li, Jianbo & Zhang, Riquan, 2011. "Partially varying coefficient single index proportional hazards regression models," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 389-400, January.
    7. Jianhua Z. Huang & Linxu Liu, 2006. "Polynomial Spline Estimation and Inference of Proportional Hazards Regression Models with Flexible Relative Risk Form," Biometrics, The International Biometric Society, vol. 62(3), pages 793-802, September.
    8. Sun, Jie & Kopciuk, Karen A. & Lu, Xuewen, 2008. "Polynomial spline estimation of partially linear single-index proportional hazards regression models," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 176-188, September.
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    Cited by:

    1. Lu, Xuewen & Pordeli, Pooneh & Burke, Murray D. & Song, Peter X.-K., 2016. "Partially linear single-index proportional hazards model with current status data," Journal of Multivariate Analysis, Elsevier, vol. 151(C), pages 14-36.
    2. Wang, Xiaoguang & Shi, Xinyong, 2014. "Robust estimation for survival partially linear single-index models," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 140-152.

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