Methods for checking the markov condition in multi-state survival data

Abstract

The inference in multi-state models is traditionally performed under a Markov assumption. This assumption claims that given the present state, the future evolution of the process is independent of the states previously visited and the transition times among them. Usually, this assumption is checked including covariates depending on the history. However, since the landmark methods of the transition probabilities proposed by de Uña-Alvarez and Meira-Machado (2015), and by Putter and Spitoni (2018) are free of the Markov assumption, they can also be used to introduce such tests (at least in the scope of the progressive multi-state models) by measuring their discrepancy to Markovian estimators. In this paper, we introduce two local tests for the Markov assumption and compare them with the usual approach based on local future-past association through simulations. An application to a clinical trial on colon cancer is included.