Product-limit estimators and Cox regression with missing cause-of-failure information

The Kaplan--Meier estimator of a survival function is used when cause of failure (censored or non-censored) is always observed. A method of survival function estimation is developed under the assumption that the failure indicators are missing completely at random (MCR). The resulting estimator is a smooth functional of the Nelson--Aalen estimators of certain cumulative transition intensities. The asymptotic properties of this estimator are derived. A simulation study shows that the proposed estimator has greater efficiency than competing MCR-based estimators. The approach is extended to the Cox model setting for the estimation of a conditional survival function given a covariate. Key words: Nelson--Aalen estimators, right censorship, incomplete data, product integral, counting processes 1 Introduction In this article we study inference from right-censored survival data in which the cause-offailure can be missing for some individuals. Let T denote the failure time of interest, Z a cova..