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Copula based dependent censoring in cure models

Author

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  • Morine Delhelle

    (UCLouvain)

  • Ingrid Van Keilegom

    (UCLouvain
    KU Leuven)

Abstract

In this paper we consider a time-to-event variable T that is subject to random right censoring, and we assume that the censoring time C is stochastically dependent on T and that there is a positive probability of not observing the event. There are various situations in practice in which this happens, and appropriate models and methods need to be considered to avoid biased estimators of the survival function or incorrect conclusions in clinical trials. In this work we propose a fully parametric mixture cure model for the bivariate distribution of (T, C), which deals with all these features. The model depends on a parametric copula and on parametric marginal distributions for T and C. A major advantage of our approach in comparison to existing approaches in the literature is that the copula which models the dependence between T and C is not assumed to be known, nor is the association parameter. Furthermore, our model allows for the identification and estimation of the cure fraction and the association between T and C, despite the fact that only the smallest of these variables is observable. Sufficient conditions are developed under which the model is identified, and an estimation procedure is proposed. The asymptotic behaviour of the estimated parameters is studied, and their finite sample performance is illustrated by means of a thorough simulation study and an analysis of breast cancer data.

Suggested Citation

  • Morine Delhelle & Ingrid Van Keilegom, 2025. "Copula based dependent censoring in cure models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 34(2), pages 361-382, June.
    • Handle: RePEc:spr:testjl:v:34:y:2025:i:2:d:10.1007_s11749-024-00961-7
    DOI: 10.1007/s11749-024-00961-7
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    References listed on IDEAS

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    1. Giacomini, Raffaella & Politis, Dimitris N. & White, Halbert, 2013. "A Warp-Speed Method For Conducting Monte Carlo Experiments Involving Bootstrap Estimators," Econometric Theory, Cambridge University Press, vol. 29(3), pages 567-589, June.
    2. Yeqian Liu & Tao Hu & Jianguo Sun, 2017. "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. 23(4), pages 626-650, October.
    3. Othus, Megan & Li, Yi & Tiwari, Ram C., 2009. "A Class of Semiparametric Mixture Cure Survival Models With Dependent Censoring," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1241-1250.
    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.
    5. Negera Wakgari Deresa & Ingrid Van Keilegom, 2024. "Copula Based Cox Proportional Hazards Models for Dependent Censoring," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(546), pages 1044-1054, April.
    6. Xuelin Huang & Robert A. Wolfe, 2002. "A Frailty Model for Informative Censoring," Biometrics, The International Biometric Society, vol. 58(3), pages 510-520, September.
    7. Deresa, Negera Wakgari & Van Keilegom , Ingrid, 2020. "Flexible parametric model for survival data subject to dependent censoring," LIDAM Reprints ISBA 2020043, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Yi Li & Ram C. Tiwari & Subharup Guha, 2007. "Mixture cure survival models with dependent censoring," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 285-306, June.
    9. C Czado & I Van Keilegom, 2023. "Dependent censoring based on parametric copulas," Biometrika, Biometrika Trust, vol. 110(3), pages 721-738.
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    Cited by:

    1. Seoyoon Cho & Matthew A. Psioda & Joseph G. Ibrahim, 2025. "Bayesian bivariate cure rate models using Gaussian copulas," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 31(3), pages 658-673, July.

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