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Partially linear single-index proportional hazards model with current status data

Author

Listed:
  • Lu, Xuewen
  • Pordeli, Pooneh
  • Burke, Murray D.
  • Song, Peter X.-K.

Abstract

A partially linear single-index proportional hazards model with current status data is introduced, where the cumulative hazard function is assumed to be nonparametric and a nonlinear link function is assumed to take a parametric spline function. Efficient estimation and effective algorithm are established. Polynomial spline smoothing is invoked for the estimation of the cumulative baseline hazard function with monotonicity constraint on the functional, while a simultaneous sieve maximum likelihood (SML) estimation is proposed to estimate regression parameters. The proposed SML estimator for the parameter vector is shown to be asymptotically normal and semiparametric efficient. The spline estimator of the functional of the cumulative hazard function is shown to achieve the optimal nonparametric rate of convergence. A simulation study is conducted to examine the finite sample performance of the proposed estimators and algorithm, and an analysis of renal function recovery data is presented.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:151:y:2016:i:c:p:14-36
    DOI: 10.1016/j.jmva.2016.06.004
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    References listed on IDEAS

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    1. Minggen Lu & Ying Zhang & Jian Huang, 2007. "Estimation of the mean function with panel count data using monotone polynomial splines," Biometrika, Biometrika Trust, vol. 94(3), pages 705-718.
    2. 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.
    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.
    4. Xuming He, 2002. "Estimation in a semiparametric model for longitudinal data with unspecified dependence structure," Biometrika, Biometrika Trust, vol. 89(3), pages 579-590, August.
    5. 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.
    6. Torben Martinussen, 2002. "Efficient estimation in additive hazards regression with current status data," Biometrika, Biometrika Trust, vol. 89(3), pages 649-658, August.
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