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Abstract:
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Many applications in medical statistics as well as in other fields can be described by transitions between multiple states (e.g. from health to disease) that individuals experience over time. Multi-state models are a popular statistical technique to deal with these types of data, in particular when the exact transition time is not observed. The main contribution of this work is to propose a joint semi-parametric model for several possibly related multi-state processes (Seemingly Unrelated Multi-State Models, SUMS), assuming a Markov structure for the transition model. The dependence between different processes is captured by specifying a joint random effect distribution on the transition rates of each process. We assume a nonparametric prior for the random effect distribution, to allow for clustering of the individuals, over dispersions and outliers. Moreover, the precision matrix of the random effect distribution is modelled conditionally to a graph which describes the dependence structure, exploiting tools from the Gaussian Graphical model literature. It is also possible to include covariates effect. SUMS provides a flexible modelling approach which finds wide applicability in l
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