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Nonparametric estimation of conditional cure models for heavy-tailed distributions and under insufficient follow-up

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  • Escobar-Bach, Mikael
  • Van Keilegom, Ingrid

Abstract

When analyzing time-to-event data, it often happens that some subjects do not experience the event of interest. Survival models that take this feature into account (called ‘cure models’) have been developed in the presence of covariates. However, the nonparametric cure models with covariates, in the current literature, cannot be applied when the follow-up is insufficient, i.e., when the right endpoint of the support of the censoring time is strictly smaller than that of the survival time of the susceptible subjects. New estimators of the conditional cure rate and the conditional survival function are proposed using extrapolation techniques coming from extreme value theory. The proposed methodology can also be used to estimate the conditional survival function when no cure rate is present. The asymptotic normality of the proposed estimators is established and their performances for small samples are shown by means of a simulation study. Their practical applicability is illustrated through the analysis of two short applications with real datasets on the repayment of student bullet loans and the employee's turnover in a company.

Suggested Citation

  • Escobar-Bach, Mikael & Van Keilegom, Ingrid, 2023. "Nonparametric estimation of conditional cure models for heavy-tailed distributions and under insufficient follow-up," Computational Statistics & Data Analysis, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:csdana:v:183:y:2023:i:c:s0167947323000397
    DOI: 10.1016/j.csda.2023.107728
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    References listed on IDEAS

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    1. Ingrid Van Keilegom & Noël Veraverbeke, 1997. "Estimation and Bootstrap with Censored Data in Fixed Design Nonparametric Regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(3), pages 467-491, September.
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    5. Mikael Escobar‐Bach & Ingrid Van Keilegom, 2019. "Non‐parametric cure rate estimation under insufficient follow‐up by using extremes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(5), pages 861-880, November.
    6. Ana López-Cheda & M. Amalia Jácome & Ricardo Cao, 2017. "Nonparametric latency estimation for mixture cure models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 353-376, June.
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    8. Justin Chown & Cédric Heuchenne & Ingrid Van Keilegom, 2020. "The nonparametric location-scale mixture cure model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 1008-1028, December.
    9. Escobar-Bach, Mikael & Van Keilegom, Ingrid, 2019. "Non-parametric cure rate estimation under insufficient follow-up by using extremes," LIDAM Reprints ISBA 2019062, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Lopez-Cheda, Ana & Cao, Ricardo & Jacome, Amalia & Van Keilegom, Ingrid, 2017. "Nonparametric incidence estimation and bootstrap bandwidth selection in mixture cure models," LIDAM Reprints ISBA 2017001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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