N elson– A alen Estimator

Abstract

Abstract It is described how the Nelson–Aalen estimator can be used to provide a nonparametric estimate of the cumulative hazard rate function based on right censored and/or left truncated survival data, and how the estimator can be used to estimate the integrated transition intensities in Markovian multistate models. It is also pointed out how the Nelson–Aalen estimator can be adopted to estimate other quantities, like the integrated relative mortality in a multiplicative model with external rates and the cumulative infection rate in a simple epidemic model. It is shown that counting processes provide a framework that allows for a unified treatment of all these diverse situations, and the most important small and large sample properties of the estimator are summarized. Finally, the construction of confidence bands is considered.