Nonparametric Cure Models Through Extreme‐Value Tail Estimation
提出一种基于极值理论的非参数方法，利用概率绘图和顶部顺序统计量联合估计治愈率和极值指数，适用于随访不足的情况，并在模拟和挪威出生登记数据中表现优于现有模型。
ABSTRACT In survival analysis, the estimation of the proportion of subjects who will never experience the event of interest, termed the cure rate, has received considerable attention recently. Its estimation can be a particularly difficult task when follow‐up is not sufficient, that is, when the censoring mechanism has a smaller support than the distribution of the target data. In the latter case, nonparametric estimators were recently proposed using extreme value methodology, assuming that the distribution of the susceptible population is in the Fréchet or Gumbel max‐domains of attraction. In this paper, we take the extreme value techniques one step further, to jointly estimate the cure rate and the extreme value index, using probability plotting methodology, and in particular using the full information contained in the top order statistics. In other words, under sufficient or insufficient follow‐up, we reconstruct the immune proportion. To this end, a Peaks‐over‐Threshold approach is proposed under the Gumbel max‐domain assumption. Next, the approach is also transferred to more specific models such as Pareto, log‐normal, and Weibull tail models, allowing to recognize the most important tail characteristics of the susceptible population. We establish the asymptotic behavior of our estimators under regularization. Though simulation studies, our estimators are shown to rival and often outperform established models, even when purely considering cure rate estimation. Finally, we provide an application of our method to Norwegian birth registry data.