Abstract
Aalen–Johansen estimation targets transition probabilities in multi-state Markov models subject to right-censoring. In particular, it belongs to the standard toolkit of statisticians specializing in health and disability. We introduce for the first time the conditional Aalen-Johansen estimator, a kernel-based estimator that allows for the inclusion of covariates and, importantly, is also applicable in non-Markov models. We establish uniform strong consistency and asymptotic normality under lax regularity conditions; here, the theory of empirical processes plays a central role and leads to a transparent treatment. We also illustrate the practical implications and strength of the estimation methodology.