Testing Markovianity in the three-state progressive model via future-past association.

The three-state progressive model is a special multi-state model with important applications in Survival Analysis. It provides a suitable representation of the individual's history when an intermediate event (with a possible influence on the survival prognosis) is experienced before the main event of interest. Estimation of transition probabilities in this and other multi-state models is usually performed through the Aalen-Johansen estimator. However, Aalen-Johansen may be biased when the underlying process is not Markov. In this paper, we provide a new approach for testing Markovianity in the three-state progressive model. The new method is based on measuring the future-past association along time. This results in a deep inspection of the process that often reveals a non-Markovian behaviour with different trends in the association measure. A test of significance for zero future-past association at each time point is introduced, and a significance trace is proposed accordingly. The finite sample performance of the test is investigated through simulations. We illustrate the new method through real data analysis.