Behavior of the Kaplan-Meier Estimator for Deterministic Imputations to Interval-Censored Data and the Turnbull Estimator

Abstract

Despite the fact that the left-point imputation for the interval-censored data produces shorter individual survival time than the right-point imputation, we observe that the Kaplan-Meier estimator based on the left-point imputation can sometimes produce greater survival rate than the right-point imputation during certain period of time interval. In practice, if the exact date of occurrence is not known due to interval-censoring, the date of examination when the event was observed is most often recorded as though the exact time of event (right-point imputation). Therefore, we investigated behavior of the deterministic imputations for the Kaplan-Meier estimator and compared with the Turnbull estimator (1976), a standard analysis of interval-censored data, by simulation. The mid-point imputation is shown to have smallest mean squared errors at most range of time under moderate to small censoring for all hazard rates investigated here, although ad hoc estimators of SE underestimate true SE. Under heavy censoring, either the right-, mid-or left-point imputations are shown to have smallest mean squared errors over certain periods. The right-point imputation (KMR) may be acceptable with large percent right-censored under increasing hazard. On the other hand, the Turnbull estimator (TB) is usually not shown to have smallest mean squared errors. We find a systematic bias of TB at tail similar to that of KMR.