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Under the assumption of random censoring, the exact bias and exact mean-square error of both the Kaplan-Meier estimator of the survival distribution and the Nelson-Aalen estimator of the hazard function are obtained and good, computationally simple bounds are derived. These bounds are useful to determine, for fixed sample size and increasing time rather than fixed time and increasing sample size, the precision of the estimators when the testing program is subject to chance sensoring. Explicit small-sample comparisons are made when the hazard of life and the hazard of censoring are proportional. General bounds are then expressed in similar terms. These results indicate that bias is lower under random censoring when life has a decreasing, and censoring an increase, hazard rate.
Luo et al. (1993) studied this question.