Institute of Mathematical Statistics Lecture Notes - Monograph Series

Non- and semi-parametric analysis of failure time data with missing failure indicators

Irene Gijbels, Danyu Lin, and Zhiliang Ying

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Abstract

A class of estimating functions is introduced for the regression parameter of the Cox proportional hazards model to allow unknown failure statuses on some study subjects. The consistency and asymptotic normality of the resulting estimators are established under mild conditions. An adaptive estimator which achieves the minimum variance-covariance bound of the class is constructed. Numerical studies demonstrate that the asymptotic approximations are adequate for practical use and that the efficiency gain of the adaptive estimator over the complete-case analysis can be quite substantial. Similar methods are also developed for the nonparametric estimation of the survival function of a homogeneous population and for the estimation of the cumulative baseline hazard function under the Cox model.

Chapter information

Source
Regina Liu, William Strawderman and Cun-Hui Zhang, eds., Complex Datasets and Inverse Problems: Tomography, Networks and Beyond (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2007), 203-223

Dates
First available in Project Euclid: 4 December 2007

Permanent link to this document
https://projecteuclid.org/euclid.lnms/1196794954

Digital Object Identifier
doi:10.1214/074921707000000166

Subjects
Primary: 62J99: None of the above, but in this section
Secondary: 62F12: Asymptotic properties of estimators 62G05: Estimation

Keywords
cause of death censoring competing risks counting process Cox model cumulative hazard function failure type incomplete data Kaplan-Meier estimator partial likelihood proportional hazards regression survival data

Rights
Copyright © 2007, Institute of Mathematical Statistics

Citation

Gijbels, Irene; Lin, Danyu; Ying, Zhiliang. Non- and semi-parametric analysis of failure time data with missing failure indicators. Complex Datasets and Inverse Problems, 203--223, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2007. doi:10.1214/074921707000000166. https://projecteuclid.org/euclid.lnms/1196794954


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