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October 2005 Asymptotic behavior of the unconditional NPMLE of the length-biased survivor function from right censored prevalent cohort data
Masoud Asgharian, David B. Wolfson
Ann. Statist. 33(5): 2109-2131 (October 2005). DOI: 10.1214/009053605000000372

Abstract

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.

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Masoud Asgharian. David B. Wolfson. "Asymptotic behavior of the unconditional NPMLE of the length-biased survivor function from right censored prevalent cohort data." Ann. Statist. 33 (5) 2109 - 2131, October 2005. https://doi.org/10.1214/009053605000000372

Information

Published: October 2005
First available in Project Euclid: 25 November 2005

zbMATH: 1086.62113
MathSciNet: MR2211081
Digital Object Identifier: 10.1214/009053605000000372

Subjects:
Primary: 62G20
Secondary: 62N02

Keywords: Censored data , consistency , informative censoring , length-biased sampling , NPMLE , prevalent cohort , survival function , weak convergence and asymptotic efficiency

Rights: Copyright © 2005 Institute of Mathematical Statistics

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Vol.33 • No. 5 • October 2005
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