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Identifiability of cure models


  • Li, Chin-Shang
  • Taylor, Jeremy M. G.
  • Sy, Judy P.


Cure models can be used for censored survival data in which a fraction of the observations do not exhibit the event of interest despite long-term follow-up. In this paper we investigate the identifiability of two forms of the cure model, a standard cure model based on a mixture distribution and a non-mixture proportional hazards (PH) model with long-term survivors. In the standard cure model, except for the case where the conditional survival function is independent of covariates and the mixture probability is an arbitrary function of a covariate we show that the parameters of the standard cure model are identified. In the non-mixture PH model, we show the model is identifiable if the distribution function is specified.

Suggested Citation

  • Li, Chin-Shang & Taylor, Jeremy M. G. & Sy, Judy P., 2001. "Identifiability of cure models," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 389-395, October.
  • Handle: RePEc:eee:stapro:v:54:y:2001:i:4:p:389-395

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    Cited by:

    1. Peng, Yingwei & Zhang, Jiajia, 2008. "Identifiability of a mixture cure frailty model," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2604-2608, November.
    2. repec:bla:biomet:v:72:y:2016:i:4:p:1348-1357 is not listed on IDEAS
    3. Yeqian Liu & Tao Hu & Jianguo Sun, 0. "Regression analysis of current status data in the presence of a cured subgroup and dependent censoring," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 0, pages 1-25.
    4. Borges, Patrick & Rodrigues, Josemar & Balakrishnan, Narayanaswamy, 2012. "Correlated destructive generalized power series cure rate models and associated inference with an application to a cutaneous melanoma data," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1703-1713.
    5. Shuangge Ma, 2011. "Additive risk model for current status data with a cured subgroup," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(1), pages 117-134, February.
    6. Hanin, Leonid & Huang, Li-Shan, 2014. "Identifiability of cure models revisited," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 261-274.
    7. Lu Wang & Pang Du & Hua Liang, 2012. "Two-Component Mixture Cure Rate Model with Spline Estimated Nonparametric Components," Biometrics, The International Biometric Society, vol. 68(3), pages 726-735, September.
    8. Christophe Van den Bulte & Raghuram Iyengar, 2011. "Tricked by Truncation: Spurious Duration Dependence and Social Contagion in Hazard Models," Marketing Science, INFORMS, vol. 30(2), pages 233-248, 03-04.
    9. Pal, Suvra & Balakrishnan, N., 2016. "Destructive negative binomial cure rate model and EM-based likelihood inference under Weibull lifetime," Statistics & Probability Letters, Elsevier, vol. 116(C), pages 9-20.
    10. repec:spr:metrik:v:81:y:2018:i:2:d:10.1007_s00184-017-0638-8 is not listed on IDEAS
    11. Gallardo, Diego I. & Bolfarine, Heleno & Pedroso-de-Lima, Antonio Carlos, 2016. "Destructive weighted Poisson cure rate models with bivariate random effects: Classical and Bayesian approaches," Computational Statistics & Data Analysis, Elsevier, vol. 98(C), pages 31-45.
    12. P. C. Lambert & P. W. Dickman & C. L. Weston & J. R. Thompson, 2010. "Estimating the cure fraction in population-based cancer studies by using finite mixture models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(1), pages 35-55.
    13. Hu, Tao & Xiang, Liming, 2016. "Partially linear transformation cure models for interval-censored data," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 257-269.
    14. He, Xuming & Xue, Hongqi & Shi, Ning-Zhong, 2010. "Sieve maximum likelihood estimation for doubly semiparametric zero-inflated Poisson models," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2026-2038, October.
    15. Yu, Binbing & Peng, Yingwei, 2008. "Mixture cure models for multivariate survival data," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1524-1532, January.
    16. repec:spr:compst:v:32:y:2017:i:2:d:10.1007_s00180-016-0660-8 is not listed on IDEAS
    17. Sheng Luo & Ciprian M. Crainiceanu & Thomas A. Louis & Nilanjan Chatterjee, 2009. "Bayesian Inference for Smoking Cessation with a Latent Cure State," Biometrics, The International Biometric Society, vol. 65(3), pages 970-978, September.
    18. repec:spr:lifeda:v:23:y:2017:i:4:d:10.1007_s10985-016-9382-z is not listed on IDEAS
    19. Hu, Tao & Xiang, Liming, 2013. "Efficient estimation for semiparametric cure models with interval-censored data," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 139-151.
    20. Li, Shuwei & Hu, Tao & Wang, Peijie & Sun, Jianguo, 2017. "Regression analysis of current status data in the presence of dependent censoring with applications to tumorigenicity experiments," Computational Statistics & Data Analysis, Elsevier, vol. 110(C), pages 75-86.


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