The Annals of Statistics

Asymptotic behavior of the unconditional NPMLE of the length-biased survivor function from right censored prevalent cohort data

Masoud Asgharian and David B. Wolfson

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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.

Article information

Source
Ann. Statist., Volume 33, Number 5 (2005), 2109-2131.

Dates
First available in Project Euclid: 25 November 2005

Permanent link to this document
https://projecteuclid.org/euclid.aos/1132936558

Digital Object Identifier
doi:10.1214/009053605000000372

Mathematical Reviews number (MathSciNet)
MR2211081

Zentralblatt MATH identifier
1086.62113

Subjects
Primary: 62G20: Asymptotic properties
Secondary: 62N02: Estimation

Keywords
Prevalent cohort censored data length-biased sampling informative censoring survival function NPMLE consistency weak convergence and asymptotic efficiency

Citation

Asgharian, Masoud; Wolfson, David B. Asymptotic behavior of the unconditional NPMLE of the length-biased survivor function from right censored prevalent cohort data. Ann. Statist. 33 (2005), no. 5, 2109--2131. doi:10.1214/009053605000000372. https://projecteuclid.org/euclid.aos/1132936558


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