On an extension of the promotion time cure model
促进时间治愈模型的一种扩展AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要研究生存分析与治愈模型，未提供归入所列计量领域细分的直接依据。
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促进时间治愈模型的一种扩展
- 研究问题
- 如何在存在删失、部分个体永不发生目标事件且含协变量的生存数据中，简化条件事件时间分布的估计与推断？
- 方法与思路
- 作者提出受 Cox 模型启发的新治愈模型，给出简便估计程序与方差闭式表达，并研究模型误设及高维正则化估计。
- 材料陈述的贡献
- 摘要称新模型包含指数链接的促进时间治愈模型，该特例估计与 Cox 部分似然估计相同，并给出渐近性质和高维误差阶。
- 阅读关注点
- 核对治愈概率与事件时间分布的模型关系、估计等价成立的条件，以及误设下的目标参数和高维误差所用度量。
- 阅读边界
- 依据版本未注明的 OpenAlex 索引摘要；摘要未说明完整正则条件、误差度量及模拟数值，不能推断其他版本的变化。
原文摘要
We consider the problem of estimating the distribution of time-to-event data that is subject to censoring and for which the event of interest might never occur, that is, 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 (Stochastic Models of Tumor Latency and Their Biostatistical Applications (1996) World Scientific), 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. In this paper, we show (i) that the new model contains as a special case the promotion time cure model with an exponential link, and hence we have a simpler way to estimate the latter model than what is done so far in the literature; (ii) that in the latter special case, both estimators are equal to the partial likelihood estimator under the usual Cox model; (iii) that the estimators under the new model have certain asymptotic properties when the model is correct and when it is misspecified; (iv) that the error of LASSO type estimators is of order log(nd)/n in the case of high-dimensional covariates with dimension d and sample size n. We also study the practical behaviour of our estimation procedure by means of simulations, and we apply our model and estimation method to a breast cancer data set.