Aalen and Johansen (1978) generalized the notion of the Product-Limit estimator or Kaplan-Meier estimator in survival analysis to the estimation of a transition matrix corresponding to a finite-state, time-continuous Markov process. Anderson, Borgen, Gill and Keiding's (1993) extended the work of Aalen and Johansen giving many detailed and varied examples illustrating the importance of this estimator. Some examples are applications to right-censored, left-truncated and competing risks models.

General bootstrap methods for the Aalen Johansen estimator are presented. In particular, these methods exhibit a martingale structure, which is key to validation of these methods and obtaining direct analytical results without simulation in some cases. This is work in progress.