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Biometrika 1992 79(3):495-512; doi:10.1093/biomet/79.3.495
© 1992 by Biometrika Trust
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Covariance and survivor function estimation using censored multivariate failure time data

R. L. PRENTICE and J. CAI

Division of Public Health Sciences, Fred Hutchinson Cancer Research Center 1124 Columbia Street, Seattle, Washington 98104, U.S.A.

The covariance between counting process martingales is used to characterize the dependence between two failure time variates. A representation of the bivariate survivor function is obtained in terms of the marginal survivor functions and this covariance function. A closely related representation expresses the bivariate survivor function in terms of marginal survivor functions and a conditional covariance function, leading to a new nonparametric survivor function estimator. Generalizations to higher dimensional failure time variates are also given. Simulation evaluations of the survivor function estimator are presented, and generalizations to regression problems are outlined.

Key Words: Censoring • Correlated failure times • Counting process • Covariance • Marginal hazard rates • Martingale • Multivariate survivor function estimation • Nonparametric estimation • Peano series • Relative risk regression • Survival data • Volterra integral equation


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