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The Identifiability of Dependent Competing Risks Models Induced by Bivariate Frailty Models

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  • Antai Wang
  • Krishnendu Chandra
  • Ruihua Xu
  • Junfeng Sun

Abstract

type="main" xml:id="sjos12114-abs-0001"> In this paper, we propose to use a special class of bivariate frailty models to study dependent censored data. The proposed models are closely linked to Archimedean copula models. We give sufficient conditions for the identifiability of this type of competing risks models. The proposed conditions are derived based on a property shared by Archimedean copula models and satisfied by several well-known bivariate frailty models. Compared with the models studied by Heckman and Honoré and Abbring and van den Berg, our models are more restrictive but can be identified with a discrete (even finite) covariate. Under our identifiability conditions, expectation–maximization (EM) algorithm provides us with consistent estimates of the unknown parameters. Simulation studies have shown that our estimation procedure works quite well. We fit a dependent censored leukaemia data set using the Clayton copula model and end our paper with some discussions. © 2014 Board of the Foundation of the Scandinavian Journal of Statistics

Suggested Citation

  • Antai Wang & Krishnendu Chandra & Ruihua Xu & Junfeng Sun, 2015. "The Identifiability of Dependent Competing Risks Models Induced by Bivariate Frailty Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 427-437, June.
    • Handle: RePEc:bla:scjsta:v:42:y:2015:i:2:p:427-437
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    References listed on IDEAS

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    1. Jaap H. Abbring & Gerard J. Van Den Berg, 2003. "The identifiability of the mixed proportional hazards competing risks model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 701-710, August.
    2. Wang, Antai, 2014. "Properties of the marginal survival functions for dependent censored data under an assumed Archimedean copula," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 57-68.
    3. Wang, Antai, 2012. "On the nonidentifiability property of Archimedean copula models under dependent censoring," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 621-625.
    4. Rivest, Louis-Paul & Wells, Martin T., 2001. "A Martingale Approach to the Copula-Graphic Estimator for the Survival Function under Dependent Censoring," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 138-155, October.
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