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Proportional hazards models for survival data with long-term survivors

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  • Zhao, Xiaobing
  • Zhou, Xian

Abstract

In this paper we study the Cox proportional hazards model for survival data in the presence of long-term survivors. Both semiparametric and full parametric versions of the Cox model are considered. Partial likelihood and full likelihood are used to obtain the estimators of the coefficients of covariates and the long-term survivor proportion. Their asymptotic properties are also derived based on counting process and martingale theory. Simulations are carried out to check and compare the performance of the estimators between semiparametric and full parametric models.

Suggested Citation

  • Zhao, Xiaobing & Zhou, Xian, 2006. "Proportional hazards models for survival data with long-term survivors," Statistics & Probability Letters, Elsevier, vol. 76(15), pages 1685-1693, September.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:15:p:1685-1693
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    References listed on IDEAS

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    1. Judy P. Sy & Jeremy M. G. Taylor, 2000. "Estimation in a Cox Proportional Hazards Cure Model," Biometrics, The International Biometric Society, vol. 56(1), pages 227-236, March.
    2. Tsodikov A.D. & Ibrahim J.G. & Yakovlev A.Y., 2003. "Estimating Cure Rates From Survival Data: An Alternative to Two-Component Mixture Models," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 1063-1078, January.
    3. Yingwei Peng & Keith B. G. Dear, 2000. "A Nonparametric Mixture Model for Cure Rate Estimation," Biometrics, The International Biometric Society, vol. 56(1), pages 237-243, March.
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    Cited by:

    1. Zhao, Xiaobing & Zhou, Xian, 2009. "Semiparametric modeling of medical cost data containing zeros," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1207-1214, May.
    2. Zhao, Xiaobing & Zhou, Xian, 2012. "Modeling gap times between recurrent events by marginal rate function," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 370-383.

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