Estimation under censoring with missing failure indicators
The Kaplan-Meier estimator of a survival function is well-known to be asymptotically efficient when cause of failure (censored or non-censored) is always observed. We consider the problem of finding an estimator when the failure indicators are missing completely at random. Under this assumption, it is known that the method of nonparametric maximum likelihood fails to work in this problem. We introduce a new estimator that is a smooth functional of the Nelson-Aalen estimators of certain cumulative transition intensities. The asymptotic distribution of the estimator is derived using the functional delta method. Simulation studies reveal that this estimator competes well with the existing estimators. The idea is extended to the Cox model, and estimators are introduced for the regression parameter and the cumulative baseline hazard function.
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