Interval-specific censoring set adjusted Kaplan-Meier estimator

We propose a non-parametric approach to reduce the overestimation of the Kaplan-Meier (KM) estimator when the event and censoring times are independent. We adjust the KM estimator based on the interval-specific censoring set, a collection of intervals where censored data are observed between two adjacent event times. The proposed interval-specific censoring set adjusted KM estimator reduces to the KM estimator if there are no censored observations or the sample size tends to infinity and the proposed estimator is consistent, as is the case for the KM estimator. We prove theoretically that the proposed estimator reduces the overestimation compared to the KM estimator and provide a mathematical formula to estimate the variance of the proposed estimator based on Greenwood's approach. We also provide a modified log-rank test based on the proposed estimator. We perform four simulation studies to compare the proposed estimator with the KM estimator when the failure rate is constant, decreasing, increasing, and based on the flexible hazard method. The bias reduction in median survival time and survival rate using the proposed estimator is considerably large, especially when the censoring rate is high. The standard deviations are comparable between the two estimators. We implement the proposed and KM estimator for the Nonalcoholic Fatty Liver Disease patients from a population study. The results show the proposed estimator substantially reduce the overestimation in the presence of high observed censoring rate.