  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)
experienced by individuals over time. In this context, multi-state models are a
popular statistical technique, in particular when the exact transition times
are not observed. The key quantities of interest are the transition rates,
capturing the instantaneous risk of moving from one state to another. The main
contribution of this work is to propose a joint semiparametric model for
several possibly related multi-state processes (Seemingly Unrelated
Multi-State, SUMS, processes), assuming a Markov structure for the transitions
over time. The dependence between different processes is captured by specifying
a joint random effect distribution on the transition rates of each process. We
assume a flexible random effect distribution, which allows for clustering of
the individuals, overdispersion and outliers. Moreover, we employ a graph
structure to describe the dependence among processes, exploiting tools from the
Gaussian Graphical model literature. It is also possible to include covariate
effects. We use our approach to model disease progression in mental health.
Posterior inference is performed through a specially devised MCMC algorithm.
