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A general approach for cure models in survival analysis

Author

Listed:
  • Patilea, Valentin
  • Van Keilegom, Ingrid

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

Abstract

In survival analysis it often happens that some subjects under study do not experience the event of interest; they are considered to be ‘cured’. The population is thus a mixture of two subpopulations : the one of cured subjects, and the one of ‘susceptible’ subjects. In this paper we propose a novel approach to estimate a mixture cure model when covariates are present and the lifetime is subject to random right censoring. We work with a parametric model for the cure proportion (like e.g. a logistic model), while the conditional survival function of the uncured subjects is unspecified. The approach is based on an inversion which allows to write the survival function as a function of the distribution of the observable random variables. This leads to a very general class of models, which allows a flexible and rich modeling of the conditional survival function. We show the identifiability of the proposed model, as well as the weak consistency and the asymptotic normality of the model parameters. We also consider in more detail the case where kernel estimators are used for the nonparametric part of the model. The new estimators are compared with the estimators from a Cox mixture cure model via finite sample simulations. Finally, we apply the new model and estimation procedure on two medical data sets.

Suggested Citation

  • Patilea, Valentin & Van Keilegom, Ingrid, 2020. "A general approach for cure models in survival analysis," LIDAM Reprints ISBA 2020042, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2020042
    DOI: https://doi.org/10.1214/19-AOS1889
    Note: In: Annals of Statistics, Vol. 48, no. 4, p. 2323-2346 (2020)
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    Citations

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    Cited by:

    1. Dirick, Lore & Claeskens, Gerda & Vasnev, Andrey & Baesens, Bart, 2022. "A hierarchical mixture cure model with unobserved heterogeneity for credit risk," Econometrics and Statistics, Elsevier, vol. 22(C), pages 39-55.
    2. Ana López-Cheda & Yingwei Peng & María Amalia Jácome, 2023. "Nonparametric estimation in mixture cure models with covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 467-495, June.
    3. Wende Clarence Safari & Ignacio López-de-Ullibarri & María Amalia Jácome, 2023. "Latency function estimation under the mixture cure model when the cure status is available," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(3), pages 608-627, July.
    4. Bo Han & Xiaoguang Wang, 2023. "Comments on: Nonparametric estimation in mixture cure models with covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 496-498, June.
    5. Minnie M. Joo & Brandon Bolte & Nguyen Huynh & Bumba Mukherjee, 2023. "Bayesian Spatial Split-Population Survival Model with Applications to Democratic Regime Failure and Civil War Recurrence," Mathematics, MDPI, vol. 11(8), pages 1-23, April.
    6. Motahareh Parsa & Ingrid Van Keilegom, 2023. "Accelerated failure time vs Cox proportional hazards mixture cure models: David vs Goliath?," Statistical Papers, Springer, vol. 64(3), pages 835-855, June.

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