Abstract
The inference in multi-state models is traditionally performed under a Markov assumption that claims that past and future of the process are independent given the present state. This assumption has an important role in the estimation of the transition probabilities. When the multi-state model is Markovian, the Aalen–Johansen estimator gives consistent estimators of the transition probabilities but this is no longer the case when the process is non-Markovian. Usually, this assumption is checked including covariates depending on the history. Since the landmark methods of the transition probabilities are free of the Markov assumption, they can also be used to introduce such tests by measuring their discrepancy to Markovian estimators. In this paper, we introduce tests for the Markov assumption and compare them with the usual approach based on the analysis of covariates depending on history through simulations. The methods are also compared with more recent and competitive approaches. Three real data examples are included for illustration of the proposed methods.
Highlights
Multi-state models are the most suitable models for the description of complex longitudinal survival data involving several events of interest
The inference in multi-state models is traditionally performed under a Markov assumption
Since the landmark methods of the transition probabilities proposed by de Una-Alvarez and Meira-Machado (2015), and by Putter and Spitoni (2018) are free of the Markov assumption, they can be used to introduce such tests by measuring their discrepancy to Markovian estimators
Summary
Multi-state models are the most suitable models for the description of complex longitudinal survival data involving several events of interest. A multistate model is a model for a stochastic process, which is characterized by a finite number of states and the possible transitions among them. The multi-state analysis deals with inference for transition intensities and transition probabilities. The inference for transition intensities often includes regression analysis which usually involves the modelling of each transition intensity separately. A popular choice is to model each transition intensity using a proportional hazards model assuming the process to. This paper was published as a part of the proceedings of the 34th International Workshop on Statistical Modelling (IWSM), Guimaraes, Portugal, 7–12 July 2019. Permission to reproduce or extract any parts of this abstract should be requested from the author(s)
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