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Goodness-of-fit tests for the cure rate in a mixture cure model

Author

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  • U U Müller
  • I Van Keilegom

Abstract

SUMMARY We consider models for time-to-event data that allow that an event, e.g., a relapse of a disease, never occurs for a certain percentage $p$ of the population, called the cure rate. We suppose that these data are subject to random right censoring and we model the data using a mixture cure model, in which the survival function of the uncured subjects is left unspecified. The aim is to test whether the cure rate $p$, as a function of the covariates, satisfies a certain parametric model. To do so, we propose a test statistic that is inspired by a goodness-of-fit test for a regression function due to Härdle & Mammen (1993). We show that the statistic is asymptotically normally distributed under the null hypothesis, that the model is correctly specified, and under local alternatives. A bootstrap procedure is proposed to implement the test. The good performance of the approach is confirmed with simulations. For illustration we apply the test to data on the times between first and second births.

Suggested Citation

  • U U Müller & I Van Keilegom, 2019. "Goodness-of-fit tests for the cure rate in a mixture cure model," Biometrika, Biometrika Trust, vol. 106(1), pages 211-227.
    • Handle: RePEc:oup:biomet:v:106:y:2019:i:1:p:211-227.
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    File URL: http://hdl.handle.net/10.1093/biomet/asy058
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    Citations

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    Cited by:

    1. 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.
    2. Ana López-Cheda & Yingwei Peng & María Amalia Jácome, 2023. "Rejoinder 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 513-520, June.
    3. 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.
    4. Ana Ezquerro & Brais Cancela & Ana López-Cheda, 2023. "On the Reliability of Machine Learning Models for Survival Analysis When Cure Is a Possibility," Mathematics, MDPI, vol. 11(19), pages 1-21, October.

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