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Biometrika 1998 85(3):561-572; doi:10.1093/biomet/85.3.561
© 1998 by Biometrika Trust
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Nonparametric estimation of successive duration times under dependent censoring

WEIJING WANG and MARTIN T. WELLS

Institute of Statistics Academia Sinica, Taipei, Taiwanwjwang{at}stat.sinica.edu.tw
Department of Social Statistics, Cornell University Ithaca, New York 14853, U.S.A.mtw1{at}cornell.edu

This paper considers nonparametric inference for duration times of two successive events. Since the second duration process becomes observable only if the first event has occurred, the length of the first duration affects the probability of the second duration being censored. Dependent censoring arises if the two duration times are correlated, which is often the case. Standard approaches to this problem fail because of dependent censoring mechanism. A new product-limit estimator for the second duration variable and a pathdependent joint survival function estimator are proposed, both modified for the dependent censoring. Properties of the estimators are discussed. An example from Lawless (1982) is studied for illustrative purposes as well as a simulation study.

Key Words: Auxiliary endpoints • Bivariate survival data • Dependent censoring • Informative censoring • Product-limit estimator • Serial failure events


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