The Annals of Statistics

Variance of the Kaplan-Meier Estimator and Its Quantiles Under Certain Fixed Censoring Models

Arthur J. Roth

Full-text: Open access

Abstract

For fixed censoring models that contain at most one intermediate censoring point, we obtain exact algebraic expressions for the asymptotic variances of (i) the quantiles of the Kaplan-Meier (KM, 1958) survival estimator and (ii) the KM estimator itself at fixed time points. The relationship between (i) and (ii) is found to be the same as the one derived by Sander (1975) and Reid (1981b) for the random censorship model. Confidence intervals for the quantiles based on (i) are briefly discussed and compared to previously known procedures. Although Greenwood's Formula is recommended over (ii) in practice because of its (desirable) conditioning on the observed censoring pattern, (ii) is of theoretical interest as an asymptotic limit for Greenwood's Formula in closed form.

Article information

Source
Ann. Statist. Volume 13, Number 3 (1985), 1230-1238.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349667

Digital Object Identifier
doi:10.1214/aos/1176349667

Mathematical Reviews number (MathSciNet)
MR803769

Zentralblatt MATH identifier
0594.62040

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62G10: Hypothesis testing 62E20: Asymptotic distribution theory 62P10: Applications to biology and medical sciences

Keywords
Fixed censoring random censoring asymptotic variance asymptotic inference density estimation survival quantiles Greenwood's formula survival distribution Kaplan-Meier estimator

Citation

Roth, Arthur J. Variance of the Kaplan-Meier Estimator and Its Quantiles Under Certain Fixed Censoring Models. Ann. Statist. 13 (1985), no. 3, 1230--1238. doi:10.1214/aos/1176349667. https://projecteuclid.org/euclid.aos/1176349667


Export citation