The Kaplan-Meier Estimate for Dependent Failure Time Observations

In some long term medical follow-up studies, a series of dependent and possibly censored failure times may be observed. Suppose that these failure times were generated from the same distribution function, and inferences about it are of our main interest. In this article, we show that under rather weak conditions for the dependence among the observations, the Kaplan-Meier estimator is still consistent and asymptotically normal. For a special dependent case in which highly stratified data are observed, a valid estimate for the limiting variance of the Kaplan-Meier estimate is also provided. Our proposal is illustrated with an examply.