Title: Non-parametric cure models through extreme-value tail estimation Show Chinese title

Title: 非参数治愈模型通过极值尾部分估计

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, non-parametric estimators were recently proposed using extreme value methodology, assuming that the distribution of the susceptible population is in the Fr\'echet 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 show 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. Show Chinese abstract

Abstract: 在生存分析中，估计永远不会经历感兴趣事件的受试者比例（称为治愈率）最近引起了相当大的关注。当随访不足时，即当删失机制的支持范围小于目标数据的分布时，这种估计可能是一个特别困难的任务。 在后一种情况下，最近提出了使用极值方法的非参数估计器，假设易感人群的分布属于Fréchet或Gumbel最大域。 在本文中，我们将极值技术进一步推进，使用概率绘图方法联合估计治愈率和极值指数，并且特别利用了顶部顺序统计量中所包含的全部信息。 换句话说，在充分或不充分的随访下，我们重构免疫比例。 为此，在Gumbel最大域假设下提出了一种基于阈值的方法。 接下来，该方法也被转移到更具体的模型中，如Pareto、对数正态和Weibull尾部模型，允许识别易感人群最重要的尾部特征。 我们在正则化条件下建立了我们估计量的渐近行为。 通过模拟研究，我们的估计器显示可以与已建立的模型相媲美，甚至常常超越这些模型，即使纯粹考虑治愈率估计也是如此。 最后，我们提供了我们的方法在挪威出生登记数据中的应用。