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

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  • Ursula U Müller
  • Ingrid Van Keilegom

Abstract

© 2018 Biometrika Trust. 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

  • Ursula U Müller & Ingrid Van Keilegom, 2018. "Goodness-of-fit tests for the cure rate in a mixture cure model," Working Papers of Department of Decision Sciences and Information Management, Leuven 630683, KU Leuven, Faculty of Economics and Business (FEB), Department of Decision Sciences and Information Management, Leuven.
    • Handle: RePEc:ete:kbiper:630683
    Note: paper number KBI_1824
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