On Consistency of the Self‐Consistent Estimator of Survival Functions with Interval‐Censored Data

The self‐consistent estimator is commonly used for estimating a survival function with interval‐censored data. Recent studies on interval censoring have focused on case 2 interval censoring, which does not involve exact observations, and double censoring, which involves only exact, right‐censored or left‐censored observations. In this paper, we consider an interval censoring scheme that involves exact, left‐censored, right‐censored and strictly interval‐censored observations. Under this censoring scheme, we prove that the self‐consistent estimator is strongly consistent under certain regularity conditions.