Cure models have been widely developed to estimate the cure fraction when some subjects never experience the event of interest. However, these models were rarely focused on the estimation of the time-to-cure, that is, the delay elapsed between the diagnosis and “the time from which cure is reached,” an important indicator, for instance, to address the question of access to insurance or loans for subjects with personal history of cancer. We propose a new excess hazard regression model that includes the time-to-cure as a covariate-dependent parameter to be estimated. The model is written similarly to a Beta probability distribution function and is shown to be a particular case of the non–mixture cure models. Parameters are estimated through a maximum likelihood approach and simulation studies demonstrate good performance of the model. Illustrative applications to three cancer data sets are provided and some limitations as well as possible extensions of the model are discussed. The proposed model offers a simple and comprehensive way to estimate more accurately the time-to-cure.

中文翻译：

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以治愈时间为参数对过度危害进行建模

当一些受试者从未经历过感兴趣的事件时，治愈模型已被广泛开发以估计治愈分数。然而，这些模型很少关注治愈时间的估计，即诊断与“达到治愈的时间”之间的延迟，这是一个重要的指标，例如，解决有个人癌症病史的受试者获得保险或贷款。我们提出了一种新的过度危险回归模型，其中包括治愈时间作为要估计的协变量相关参数。该模型的编写类似于 Beta 概率分布函数，并显示为非混合物固化模型的一个特例。参数是通过最大似然法估计的，模拟研究表明模型具有良好的性能。提供了对三个癌症数据集的说明性应用，并讨论了模型的一些限制以及可能的扩展。所提出的模型提供了一种简单而全面的方法来更准确地估计固化时间。