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The Kaplan-Meier estimate for dependent failure time observations. (English) Zbl 0798.62048

Summary: 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.
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 example.

MSC:

62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
62P10 Applications of statistics to biology and medical sciences; meta analysis
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