Nonparametric Estimation from Cross-Sectional Survival Data
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横截面生存数据的非参数估计
- 研究问题
- 在横截面抽样导致左截断、同时存在右删失的生存数据中，如何估计截断分布并开展渐近推断和自助抽样？
- 方法与思路
- 作者采用工作数据思路与非参数得分函数，研究乘积极限估计，并推导截断分布及截断与删失联合分布的估计。
- 材料陈述的贡献
- 摘要称相关估计可用于检验平稳性、估计截断比例，并将针对右删失数据的 Efron 自助法扩展到同时左截断的数据。
- 阅读关注点
- 应核对截断、删失与生存变量的关系假设，平稳性检验的构造，以及联合分布估计如何支持自助抽样程序。
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- 仅有 OpenAlex 索引摘要，稿件版本未注明；依赖条件和效率比较未展开，不能把文中转述的效率期待当成已证实优势或推断刊本变化。
原文摘要
In many follow-up studies survival data are often observed according to a cross-sectional sampling scheme. Data of this type are subject to left truncation in addition to the usual right censoring. A number of characteristics and properties of the product-limit estimate, for left-truncated and right-censored data, have been explored and found to be similar to those of the Kaplan-Meier estimate. Under the stationarity assumption, however, it is believed that an alternative estimate has much better efficiency. In this article the conditional maximum likelihood estimate (MLE) property of the product-limit estimate is visited. The non-parametric MLE of the truncation distribution is derived. Use of this estimate includes testing the stationarity assumption, estimating the proportion of truncated data, and other applications in prevalent cohort studies. The analysis of the estimation is based on a “working data” approach. The asymptotic properties of the proposed estimates are developed through nonparametric score functions. It is presented that nonparametric conditional score functions possess properties similar to those of parametric conditional score functions. This observation leads to simplification of the asymptotic results. The nonparametric MLE of the joint distribution of truncation and censoring variables is also derived. This nonparametric estimate together with the product-limit estimate are used to generalize Efron's “obvious method” of bootstrapping, for right-censored data, to data that are both left truncated and right censored.