Goodness-of-fit tests for the cure rate in a mixture cure model
针对混合治愈模型中的治愈率是否满足特定参数模型，提出一种基于回归函数拟合优度检验的统计量，并证明其渐近正态性，通过模拟和生育间隔数据验证了方法的有效性。
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.