Bivariate Survival Models Induced by Frailties
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由共享脆弱性诱导的二元生存模型
- 研究问题
- 共享未观测脆弱性经比例风险机制诱导何种二元生存关联，如何容纳负关联，并从可观测分布识别脆弱性分布？
- 方法与思路
- 作者利用交叉比函数刻画二元生存分布类，扩展模型以允许负关联，并构造适用于删失数据的推断程序和诊断图。
- 材料陈述的贡献
- 摘要称，可观测二元分布能将脆弱性分布识别到尺度参数，交叉比函数连接刻画、推断与诊断，并有真实实例展示。
- 阅读关注点
- 应核对负关联扩展的机制、识别到尺度的条件、删失要求与交叉比估计方法，并区分已完成结果和提出的扩展方向。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明。研究限于单一二元分布的随机样本；高维和协变量扩展仅被提出为可能性，未给出结果。
原文摘要
When two observed survival times depend via a proportional-hazards model on the same unobserved variable, called a frailty, this common dependence induces an association between the observed times. This article considers the class of bivariate survival distributions that can arise in this way, extends it to allow negative association, and shows that the observable bivariate distribution determines the unobserved frailty distribution up to a scale parameter. A cross-ratio function, easily estimated even from censored data, is the key to both the characterization results and inferential procedures and diagnostic plots that are introduced and illustrated by real examples. The models considered are the natural counterpart for survival data of the latent variable models that have long been used in factor analysis for continuous data or in latent structure analysis for binary data. The main distinguishing feature of survival data is the possibility of censoring, which makes the standard methods difficult to apply. The procedures developed here work well with censored data. Although the present work is restricted to problems involving a random sample from a single bivariate distribution, extensions to problems involving higher-dimensional distributions and/or additional measured covariates are undoubtedly possible.