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Biometrika 1995 82(1):127-138; doi:10.1093/biomet/82.1.127
© 1995 by Biometrika Trust
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Estimates of marginal survival for dependent competing risks based on an assumed copula

MING ZHENG1 and JOHN P. KLEIN2

1Department of Statistics, The Ohio State University Columbus, Ohio 43210, U. S.A
2Department of Biostatistics, The Medical College of Wisconsin 8701 WWatertown Plank Road, Milwaukee, Wisconsin 53226, U.S.A

When time to death and time to censoring are associated one may be appreciably misled when the marginal survival functions are estimated using the product-limit estimators, which assume independent censoring. If no assumption about the relationship between the two times is made, the marginal survival functions are not identifiable. A natural function that defines the association between the two random variables is the copula. We show that if this function is known then the competing risks data are suflScient to identify the marginal survival functions and construct a suitable estimator. This estimator is consistent and reduces to the Kaplan-Meier estimator when death and censoring times are independent. This statistic can be used to provide bounds on the marginal survival functions based on a range of possible associations between the competing risks.

Key Words: Censored data • Competing risks • Copula • Identifiability • Survival function


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