Covariance and survivor function estimation using censored multivariate failure time data

SUMMARY 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.