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Polynomial spline estimation of partially linear single-index proportional hazards regression models

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  • Sun, Jie
  • Kopciuk, Karen A.
  • Lu, Xuewen

Abstract

The Cox proportional hazards (PH) model usually assumes linearity of the covariates on the log hazard function, which may be violated because linearity cannot always be guaranteed. We propose a partially linear single-index proportional hazards regression model, which can model both linear and nonlinear covariate effects on the log hazard in the proportional hazards model. We adopt a polynomial spline smoothing technique to model the structured nonparametric single-index component for the nonlinear covariate effects. This method can reduce the dimensionality of the covariates being modeled, while, at the same time, can provide efficient estimates of the covariate effects. A two-step iterative algorithm to estimate the nonparametric component and the covariate effects is used for facilitating implementation. Asymptotic properties of the estimators are derived. Monte Carlo simulation studies are presented to compare the new method with the standard Cox linear PH model and some other comparable models. A case study with clinical trial data is presented for illustration.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:53:y:2008:i:1:p:176-188
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    References listed on IDEAS

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    1. Gørgens, Tue, 2004. "Average Derivatives For Hazard Functions," Econometric Theory, Cambridge University Press, vol. 20(3), pages 437-463, June.
    2. Nielsen, Jens P. & Linton, Oliver & Bickel, Peter J., 1998. "On a semiparametric survival model with flexible covariate effect," LSE Research Online Documents on Economics 301, London School of Economics and Political Science, LSE Library.
    3. 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.
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    Cited by:

    1. 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.
    2. Ming-Yueh Huang & Kwun Chuen Gary Chan, 2022. "Model selection among Dimension-Reduced generalized Cox models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(3), pages 492-511, July.
    3. Ma, Shujie & Liang, Hua & Tsai, Chih-Ling, 2014. "Partially linear single index models for repeated measurements," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 354-375.
    4. Huang, Zhensheng & Pang, Zhen, 2012. "Corrected empirical likelihood inference for right-censored partially linear single-index model," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 276-284.
    5. 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.
    6. Raheem, S.M. Enayetur & Ahmed, S. Ejaz & Doksum, Kjell A., 2012. "Absolute penalty and shrinkage estimation in partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 874-891.
    7. 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.
    8. Myeonggyun Lee & Andrea B. Troxel & Mengling Liu, 2024. "Partial-linear single-index transformation models with censored data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 30(4), pages 701-720, October.
    9. Lian, Heng & Li, Jianbo & Hu, Yuao, 2013. "Shrinkage variable selection and estimation in proportional hazards models with additive structure and high dimensionality," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 99-112.
    10. Lin Liu & Jianbo Li & Riquan Zhang, 2014. "General partially linear additive transformation model with right-censored data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(10), pages 2257-2269, October.
    11. 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.
    12. Chin-Shang Li & Minggen Lu, 2018. "A lack-of-fit test for generalized linear models via single-index techniques," Computational Statistics, Springer, vol. 33(2), pages 731-756, June.

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