Robust Bias Estimation for Kaplan-Meier Survival Estimator with Jackknifing

For studying or reducing the bias of functionals of the Kaplan-Meier survival estimator, the jackknifing approach of Stute and Wang (1994) is natural. We have studied the behavior of the jackknife estimate of bias under different configurations of the censoring level, sample size, and the censoring and survival time distributions. The empirical research reveals some new findings about robust calculation of the bias, particularly for higher censoring levels. We have extended their jackknifing approach to cover the case where the largest observation is censored, using the imputation methods for the largest observations proposed in Khan and Shaw (2013b). 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 that the Kaplan--Meier estimator can be badly underestimated by the existing jackknife formula.