Empirical comparisons between Kaplan-Meier and Nelson-Aalen survival function estimators

The Kaplan-Meier is the most commonly used estimator of the survival function, while the Nelson-Aalen is an alternative estimator for the same function. There are many asymptotic results for these estimators in the literature. In particular, it is known that they are asymptotically equivalent. On the other hand empirical results comparing these estimators are difficult to obtain and they are necessary to guide applied statisticians. This paper addresses small-sample properties of these survival function estimators. Monte Carlo simulations are performed in order to compare both estimators. Percentile and survival fraction estimates of the survival function are used to attain this goal. The results show a slight superiority in favor of the Nelson-Aalen estimator in survival fraction estimation. However for percentile estimation the Kaplan-Meier estimator presents a better performance for decreasing failure rates while the Nelson-Aalen estimator provides better results for increasing failure rates.