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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/3307

Title: Bootstrapping in survival analysis
Authors: VERAVERBEKE, Noel
Issue Date: 1997
Publisher: SOUTH AFRICAN STATISTICAL ASSOC
Citation: SOUTH AFRICAN STATISTICAL JOURNAL, 31(2). p. 217-258
Abstract: In this survey we consider the model of right random censorship in which the quantity of primary interest is the lifetime distribution function F. Kaplan and Meier (1958) derived a nonparametric maximum likelihood estimator F-n for F, which is a natural generalization of the empirical distribution function in the complete data case. It was Efron (1981) who first proposed procedures for the construction of bootstrap observations, which then produce a bootstrapped version F-n* of F-n. We discuss the properties of F-n and F-n(*) which lead to the important consistency result: almost surely, as n --> infinity, the process n(1/2)(F-n* - F-n) converges weakly to the same Gaussian limit as the original Kaplan-Meier process n(1/2)(F-n - F). We also deal with the analogous properties for the corresponding quantile processes. Moreover, we consider the question of accuracy of the bootstrap approximation. Finally, we look into the situation of regression models which study the effect of covariates on the distributions of the lifetimes. We consider bootstrap procedures for the regression parameter in Cox's proportional hazards model and for Beran's distribution function estimator in a fixed design nonparametric regression model.
Notes: Limburgs Univ Ctr, B-3590 Diepenbeek, Belgium.
URI: http://hdl.handle.net/1942/3307
ISI #: 000072016400004
ISSN: 0038-271X
Type: Journal Contribution
Validation: ecoom, 1999
Appears in Collections: Research publications

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