A alen– J ohansen Estimator

Abstract The Aalen–Johansen estimator is a matrix version of the Kaplan–Meier estimator, and it 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 simple Markov processes, the elements of the Aalen–Johansen estimator take an explicit form. Then, the estimator is described for a general finite state Markov process, modeling the life histories of individuals from a homogeneous population. It is shown how the Aalen–Johansen estimator may be obtained as the product integral of the matrix of Nelson–Aalen estimators for the cumulative transition intensities, and it is briefly indicated how the product‐integral formulation of the Aalen–Johansen estimator is useful for the study of its statistical properties. Finally, estimation of state occupation probabilities is discussed and extensions to regression models are mentioned.