Abstract |
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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 test proposed by Härdle and Mammen in the context of goodness-of-fit tests for a regression function. We show that the test statistic is asymptotically normally distributed under the null hypothesis that the model is correctly specified. A bootstrap procedure is proposed to implement the test. The good performance of the approach is confirmed with simulations: we test whether the logistic curve is an adequate model for p, and also whether a cure proportion p exists at all. For an illustration we apply the test to data on the times between first and second birth. |