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A two‐step estimation procedure for semiparametric mixture cure models

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  • Eni Musta
  • Valentin Patilea
  • Ingrid Van Keilegom

Abstract

In survival analysis, cure models have been developed to account for the presence of cured subjects that will never experience the event of interest. Mixture cure models with a parametric model for the incidence and a semiparametric model for the survival of the susceptibles are particularly common in practice. Because of the latent cure status, maximum likelihood estimation is performed via the iterative EM algorithm. Here, we focus on the cure probabilities and propose a two‐step procedure to improve upon the maximum likelihood estimator when the sample size is not large. The new method is based on presmoothing by first constructing a nonparametric estimator and then projecting it on the desired parametric class. We investigate the theoretical properties of the resulting estimator and show through an extensive simulation study for the logistic‐Cox model that it outperforms the existing method. Practical use of the method is illustrated through two melanoma datasets.

Suggested Citation

  • Eni Musta & Valentin Patilea & Ingrid Van Keilegom, 2024. "A two‐step estimation procedure for semiparametric mixture cure models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(3), pages 987-1011, September.
    • Handle: RePEc:bla:scjsta:v:51:y:2024:i:3:p:987-1011
    DOI: 10.1111/sjos.12713
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    References listed on IDEAS

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    1. 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).
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    6. Rebeca Peláez Suárez & Ricardo Cao Abad & Juan M. Vilar Fernández, 2021. "Probability of default estimation in credit risk using a nonparametric approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 383-405, June.
    7. Lorenzo Tedesco & Jad Beyhum & Ingrid Van Keilegom, 2023. "Instrumental variable estimation of the proportional hazards model by presmoothing," Papers 2309.02183, arXiv.org.
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    9. Amico, Mailis & Van Keilegom, Ingrid & Legrand, Catherine, 2019. "The Single-Index/Cox Mixture Cure Model," LIDAM Reprints ISBA 2019007, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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