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For reducing bias of functionals of the Kaplan-Meier survival estimator, the jackknifing approach as proposed by Stute and Wang is a natural choice. We have extended their jackknifing approach to cover the case where the largest observation is censored by using different imputation approaches of the largest censored observations as proposed by Khan and Shaw. This modification to the existing formula reduces the number of conditions for creating jackknife bias estimates to one from the original two, and also avoids the problem in which the Kaplan-Meier estimator can be badly underestimated by the existing jackknife formula. Furthermore, we have studied broadly the behavior of the jackknife estimate of bias under varying configurations of censoring level, sample size, and distribution of censoring time and lifetime. This empirical research has explored some new findings about the robust calculation of bias particularly when censoring level is high-for example, the bias tends to zero as the censoring level tends to 100% although in the normal case the bias is zero as the censoring level is 0%.

Robust bias estimation for Kaplan–Meier survival estimator with jackknifing