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Biometrika 1996 83(3):491-506; doi:10.1093/biomet/83.3.491
© 1996 by Biometrika Trust
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On assessing the strength of dependency between failure time variates

LI HSU and ROSS L. PRENTICE

Division of Public Health Sciences, Fred Hutchinson Cancer Research Center 1124 Columbia Street, Seattle, Washington 98104, USA

The correlation p between cumulative hazard variates is considered as a measure of dependence between pairs of failure time variates. Such correlation is readily estimated in the absence of censorship, but modelling assumptions are required for its estimation in the presence of independent right censorship. A semiparametric class of bivariate failure time models, in which a dependence parameter is in one-to-one correspondence with the cumulative hazard variate correlation p, is considered for this purpose. A simple estimating function, consisting of a weighted sum over the grid formed by the observed failure times of differences between nonparametric and model-restricted estimates of covariance rates, is proposed for estimation and corresponding asymptotic distribution theory is given. This estimation procedure is shown to lack robustness under conditions of moderate to heavy censorship, motivating consideration of dependency measures that can be defined on the support of the observed failure times. Two such measures, the correlation between marginal martingales, and a cumulative cross ratio statistic, are discussed and corresponding nonparametric estimators are proposed.

Key Words: Bivariate failure time data • Censoring • Clayton bivariate survival model • Correlated failure times • Covariance function • Cumulative hazard variate correlation • Frank bivariate survival model • Marginal martingale • Nonparametric estimation • Semiparametric estimation


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