推广的推广时间治愈模型
On an extension of the promotion time cure model
摘要：
我们考虑估计受删失影响的事件发生时间数据的分布的问题，对于这些数据，感兴趣的事件可能永远不会发生，即，有些人被治愈了为了在存在协变量的情况下对此类数据建模，主要的半参数模型之一是促进时间治愈模型\citep{yakovlev1996}，该模型使Cox模型适应治愈受试者的存在。估计的条件分布的结果是一个复杂的约束最优化问题，推理是困难的，因为没有封闭的公式的方差。我们提出了一个新的模型，灵感来自Cox模型，导致一个简单的估计过程，并提出了一个闭公式的方差。我们推导出一些渐近性质的估计，我们通过模拟显示我们的程序的实际行为。我们还将我们的模型和估计方法应用于乳腺癌数据集。
英文摘要：
We consider the problem of estimating the distribution of time-to-event data that are subject to censoring and for which the event of interest might never occur, i.e., some subjects are cured. To model this kind of data in the presence of covariates, one of the leading semiparametric models is the promotion time cure model \citep{yakovlev1996}, which adapts the Cox model to the presence of cured subjects. Estimating the conditional distribution results in a complicated constrained optimization problem, and inference is difficult as no closed-formula for the variance is available. We propose a new model, inspired by the Cox model, that leads to a simple estimation procedure and that presents a closed formula for the variance. We derive some asymptotic properties of the estimators and we show the practical behaviour of our procedure by means of simulations. We also apply our model and estimation method to a breast cancer data set.
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