| Summary: | Multi-state models can be successfully used for modelling complex event history data. In these models the estimation of the transition probabilities is of particular interest, since they allow for long-term predictions of the process. These quantities have been traditionally estimated by the Aalen-Johansen estimator, which is consistent if the process is Markovian. Several non-Markovian estimators have been proposed in the recent literature, and their superiority relative to the Aalen-Johansen estimator has been demonstrated in situations in which the Markov condition is strongly violated. However, the existing estimators have the drawback of requiring the support of the censoring distribution to contain the support of the lifetime distribution, which is not often the case. In this paper we propose two new methods for estimating the transition probabilities in the progressive illness-death model, and some asymptotic results are derived. The proposed estimators are consistent regardless the Markov condition and the referred assumption on the censoring support. We explore the finite sample behavior of the estimators through simulations. The main conclusion of this work is that the proposed estimators may be much more effi cient than the existing non-Markov estimators. An application to a clinical trial on colon cancer is included. Extensions to progressive processes beyond the three-state illness-death model are discussed.
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