Published Online: 15 JUL 2005
Copyright © 2005 John Wiley & Sons, Ltd
Encyclopedia of Biostatistics
How to Cite
Borgan, Ø. 2005. Aalen–Johansen Estimator. Encyclopedia of Biostatistics.
- Published Online: 15 JUL 2005
The Aalen–Johansen estimator is a matrix version of the Kaplan–Meier estimator, which can be used to estimate the transition probability matrix of a Markov process with a finite number of states. The estimator is first presented for the competing risks model and the Markov illness–death model for a chronic disease. For these two simple Markov processes, the elements of the Aalen–Johansen estimator take an explicit form. Then a general finite state Markov process, modeling the life histories of individuals from a homogeneous population, is considered. It is described how the Aalen–Johansen estimator may be obtained as the product-integral of the matrix of Nelson–Aalen estimators for the cumulative transition intensities. Finally, it is briefly indicated how the product-integral formulation of the Aalen–Johansen estimator is useful for the study of its statistical properties.
- competing risks;
- cumulative incidence function;
- illness–death model;
- Kaplan–Meier estimator;
- multistate models;
- Nelson–Aalen estimator;
- product-limit estimator;