Alternative representations of the Aalen‐Johansen estimator of the state occupation probabilities in multi‐state models

Multi‐state models are a flexible framework for analysing processes that evolve through different states over time, with applications in medicine, demography, and economics, among others. A key quantity of interest is the state occupation probability, commonly estimated by the Aalen‐Johansen estimator. In this article, we provide alternative representations of this estimator by extending both the redistribution‐to‐the‐right algorithm and the inverse probability of censoring weighted (IPCW) empirical average representation to the general multi‐state setting. We show that these formulations are mathematically equivalent to the Aalen‐Johansen estimator, offering new interpretative insights and practical understanding.