Asymptotic behavior of the unconditional NPMLE of the length-biased survivor function from right censored prevalent cohort data
Asymptotic behavior of the unconditional NPMLE of the length-biased survivor function from right censored prevalent cohort data
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DOI：
10.1214/009053605000000372
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发表时间：
2005-10-01
影响因子：
4.5
通讯作者：
Wolfson, DB
中科院分区：
文献类型：
--
作者：
Asgharian, M;Wolfson, DB
在具有恒定发病率的流行病例队列中收集的右删失生存数据具有长度偏倚，并且可以用于估计长度偏倚（即，prevalent-case）生存函数。当发生率是常数时，即所谓的发生率平稳性，使用这种结构进行无条件统计推断比通过观察到的截断时间进行分析更有效。众所周知，由于流行队列数据的信息删失，Kaplan-Meier估计量不是长度偏倚生存函数的无条件NPMLE，并且NPMLE的渐近性质不遵循任何已知结果。我们在这里提出了一个详细的推导的NPMLE的长度偏置生存函数的渐近性质，从右删失的流行队列生存数据随访。特别是，我们证明了NPMLE是一致强一致的，弱收敛到高斯过程，并且是渐近有效的。这些结果的一个重要副产品是，它们产生了事件情况下生存函数的NPMLE的渐近性质[见Asgharian，M 'Lan和Wolfson J. Amer Statist。Assoc.97（2002）201-209]，这通常是流行队列研究中的主要兴趣。我们的结果推广了Vardi和Zhang [Ann. Statistist. 20（1992）1022-1039]，我们显示在流行队列设置中作为退化情况出现。
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.