Asymptotic behavior of the unconditional NPMLE of the length-biased survivor function from right censored prevalent cohort data
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右删失现患队列中长度偏倚生存函数无条件非参数最大似然估计的渐近行为
- 研究问题
- 在发病率恒定、具有随访与右删失的现患队列中，长度偏倚生存函数的无条件非参数最大似然估计有哪些渐近性质？
- 方法与思路
- 作者利用恒定发病率结构开展无条件推断，推导长度偏倚生存函数估计的渐近性质，并联系新发病例的生存函数估计。
- 材料陈述的贡献
- 摘要称，该估计具有一致强收敛、向高斯过程的弱收敛及渐近效率，且结果可导出新发病例生存函数估计的渐近性质。
- 阅读关注点
- 应核对恒定发病率与删失机制的形式条件、似然及估计对象、弱收敛所用空间，以及效率比较的参照框架。
- 阅读边界
- 仅据稿件版本未注明的 OpenAlex 摘要；完整抽样与删失条件未说明，无条件推断的效率结论不能推广至任意现患队列。
原文摘要
Right censored survival data collected on a cohort of prevalent cases with constant incidence are length-biased, and may be used to estimate the length-biased (i.e., prevalent-case) survival function. When the incidence rate is constant, so-called stationarity of the incidence, it is more efficient to use this structure for unconditional statistical inference than to carry out an analysis by conditioning on the observed truncation times. It is well known that, due to the informative censoring for prevalent cohort data, the Kaplan–Meier estimator is not the unconditional NPMLE of the length-biased survival function and the asymptotic properties of the NPMLE do not follow from any known result. We present here a detailed derivation of the asymptotic properties of the NPMLE of the length-biased survival function from right censored prevalent cohort survival data with follow-up. In particular, we show that the NPMLE is uniformly strongly consistent, converges weakly to a Gaussian process, and is asymptotically efficient. One important spin-off from these results is that they yield the asymptotic properties of the NPMLE of the incident-case survival function [see Asgharian, M’Lan and Wolfson J. Amer. Statist. Assoc. 97 (2002) 201–209], which is often of prime interest in a prevalent cohort study. Our results generalize those given by Vardi and Zhang [Ann. Statist. 20 (1992) 1022–1039] under multiplicative censoring, which we show arises as a degenerate case in a prevalent cohort setting.