Nelson–Aalen estimator

Summary

The Nelson–Aalen estimator is a nonparametric estimator of the cumulative hazard function from right-censored data. At each observed event time it adds the number of events divided by the number of subjects at risk. It is the natural estimator in the counting process approach to survival analysis, where its large-sample theory follows from martingale results. Taking $e^{-\hat H(t)}$ gives an estimator of the survival function close to the Kaplan–Meier estimator.