We consider the survival function for univariate right-censored event time data, when a cure fraction is present. This means that the population consists of two parts: the cured or non-susceptible group, who will never experience the event of interest versus the non-cured or susceptible group, who will undergo the event of interest when followed up sufficiently long. When modeling the data, a parametric form is often imposed on the survival function of the susceptible group. In this paper, we construct a simple novel test to verify the aptness of the assumed parametric form. To this end, we contrast the parametric fit with the nonparametric fit based on a rescaled Kaplan–Meier estimator. The asymptotic distribution of the two estimators and of the test statistic are established. The latter depends on unknown parameters, hence a bootstrap procedure is applied to approximate the critical values of the test. An extensive simulation study reveals the good finite sample performance of the developed test. To illustrate the practical use, the test is also applied on two real-life data sets.

中文翻译：

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具有治愈分数的参数生存函数的拟合优度检验

当治愈率存在时，我们考虑生存函数的单变量右删失事件时间数据。这意味着该人群由两部分组成：治愈或不敏感的人群（从未经历过关注的事件）与非治愈或易感人群（在接受足够长的随访后将经历关注的事件）。在对数据建模时，通常将参数形式强加给易感人群的生存功能。在本文中，我们构建了一个简单的新颖测试来验证假定参数形式的适用性。为此，我们将基于重新缩放的Kaplan-Meier估计量的参数拟合与非参数拟合进行对比。建立了两个估计量和检验统计量的渐近分布。后者取决于未知参数，因此，应使用引导程序来近似测试的临界值。广泛的仿真研究表明，开发的测试具有良好的有限样本性能。为了说明实际用途，该测试还应用于两个实际数据集。