A simple hybrid variance estimator for the Kaplan-Meier survival function.

In this paper, we propose a hybrid variance estimator for the Kaplan-Meier survival function. This new estimator approximates the true variance by a Binomial variance formula, where the proportion parameter is a piecewise non-increasing function of the Kaplan-Meier survival function and its upper bound, as described below. Also, the effective sample size equals the number of subjects not censored prior to that time. In addition, we consider an adjusted hybrid variance estimator that modifies the regular estimator for small sample sizes. We present a simulation study to compare the performance of the regular and adjusted hybrid variance estimators to the Greenwood and Peto variance estimators for small sample sizes. We show that on average these hybrid variance estimators give closer variance estimates to the true values than the traditional variance estimators, and hence confidence intervals constructed with these hybrid variance estimators have more nominal coverage rates. Indeed, the Greenwood and Peto variance estimators can substantially underestimate the true variance in the left and right tails of the survival distribution, even with moderately censored data. Finally, we illustrate the use of these hybrid and traditional variance estimators on a data set from a leukaemia clinical trial.