Comparison Of Nonparametric Survival Estimators For Interval-Censoring Mixed With Right-Censoring Type I: A Simulation Study

The aim of this study is to compare the performance of survival function estimators in mixed censoring between interval-censoring and right censoring type I with 20%, and 40%, via the two nonparametric methods of Kaplan-Meier and Turnbull. The Kaplan-Meier estimator is applied to the mid-point imputation. The survival function estimated by the Turnbull is a decreasing step function defined on the complement of the union of disjoint intervals, called Turnbull interval. We assume the estimate of survival function by the linear interpolation, upper bound and lower bound on each Turnbull interval. Under the conditions of our simulation study, the Kaplan-Meier estimator gives the smallest mean square error and the Turnbull estimator with linear interpolation gives a smaller mean square error than the other Turnbull estimators. Moreover, the results also show that the bias of the Turnbull estimator (mostly Turnbull estimator with linear interpolation) yield the smallest value when time between visits are 0.5 years and 1 year but the Kaplan-Meier estimator gives the smallest bias for 2 years between visits.