生存分析中的长期尾部建模：基于扩展广义帕累托分布

中文摘要 AI 辅助

我们针对右删失生存数据提出了一类扩展广义帕累托模型，特别关注尾部推断和长期外推。我们的框架整合了极值理论与生存分析，将广义帕累托分布与单位区间上的灵活扰动分布相结合。我们考虑了三种扰动设定：参数化Beta模型、伯恩斯坦多项式估计器和基于直方图的估计器。为了便于直接比较，所有三种模型均通过统一迭代程序拟合，该程序通过基于Kaplan-Meier的伪观测值适应右删失。一项蒙特卡洛研究评估了不同尾部指数、删失水平、样本量和模型复杂度下的有限样本性能。结果揭示了灵活性与稳定性之间的权衡：Beta设定在尾部指数估计方面通常表现最佳，而直方图估计器在低删失水平下的尺度估计方面表现尤为出色。伯恩斯坦估计器表现出中等性能，且对样本量和删失更为敏感。应用于膀胱癌复发和心力衰竭生存数据的实例表明，样本内拟合非常相似的模型仍可能产生显著不同的尾部指数估计和长期外推结果。这些发现强调了在使用扩展广义帕累托模型进行删失条件下生存外推时，扰动设定选择的重要性。

英文摘要

We propose a class of extended generalized Pareto models for right-censored survival data, with particular emphasis on tail inference and long-term extrapolation. Our framework integrates extreme value theory and survival analysis, combining a generalized Pareto distribution with a flexible perturbation distribution on the unit interval. We consider three perturbation specifications: a parametric Beta model, a Bernstein polynomial estimator, and a histogram-based estimator. To facilitate direct comparison, all three models are fitted using a unified iterative procedure adapted to right censoring through Kaplan-Meier-based pseudo-observations. A Monte Carlo study evaluates finite-sample performance across different tail indices, censoring levels, sample sizes, and model complexities. The results reveal a trade-off between flexibility and stability: the Beta specification generally performs best for tail-index estimation, whereas the histogram estimator performs particularly well for scale estimation under low censoring. The Bernstein estimator shows intermediate performance and greater sensitivity to sample size and censoring. Applications to bladder cancer recurrence and heart-failure survival data show that models with very similar in-sample fits can nevertheless produce markedly different tail-index estimates and long-term extrapolations. These findings emphasize the importance of perturbation specification when extended generalized Pareto models are used for survival extrapolation under censoring.

发表机构

• Universidade de São Paulo（圣保罗大学）
• Faculdade de Ciências, Universidade de Lisboa（里斯本大学理学院）

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