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April 2003 Current status and right-censored data structures when observing a marker at the censoring time
Mark J. Van der Laan, Nicholas P. Jewell
Ann. Statist. 31(2): 512-535 (April 2003). DOI: 10.1214/aos/1051027879

Abstract

We study nonparametric estimation with two types of data structures. In the first data structure n i.i.d. copies of $(C,N(C))$ are observed, where N is a finite state counting process jumping at time-variables of interest and C a random monitoring time. In the second data structure n i.i.d. copies of $(C\wedge T,I(T\leq C),N (C\wedge T))$ are observed, where N is a counting process with a final jump at time T (e.g., death). This data structure includes observing right-censored data on T and a marker variable at the censoring time.

In these data structures, easy to compute estimators, namely (weighted)-pool-adjacent-violator estimators for the marginal distributions of the unobservable time variables, and the Kaplan-Meier estimator for the time T till the final observable event, are available. These estimators ignore seemingly important information in the data. In this paper we prove that, at many continuous data generating distributions the ad hoc estimators yield asymptotically efficient estimators of $\sqrt{n}$-estimable parameters.

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Mark J. Van der Laan. Nicholas P. Jewell. "Current status and right-censored data structures when observing a marker at the censoring time." Ann. Statist. 31 (2) 512 - 535, April 2003. https://doi.org/10.1214/aos/1051027879

Information

Published: April 2003
First available in Project Euclid: 22 April 2003

zbMATH: 1039.62095
MathSciNet: MR1983540
Digital Object Identifier: 10.1214/aos/1051027879

Subjects:
Primary: 62G07
Secondary: 62F12

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.31 • No. 2 • April 2003
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