A Bayesian multivariate spatial approach for illness-death survival models.

Illness-death models are a class of stochastic models inside the multi-state framework. In those models, individuals are allowed to move over time between different states related to illness and death. They are of special interest when working with non-terminal diseases, as they not only consider the competing risk of death but also allow us to study the progression from illness to death. The intensity of each transition can be modelled including both fixed and random effects of covariates. In particular, spatially structured random effects or their multivariate versions can be used to assess spatial differences between regions and among transitions. We propose a Bayesian methodological framework based on an illness-death model with a multivariate Leroux prior for the random effects. We apply this model to a cohort study regarding progression after an osteoporotic hip fracture in elderly patients. From this spatial illness-death model, we assess the geographical variation in risks, cumulative incidences and transition probabilities related to recurrent hip fracture and death. Bayesian inference is done via the integrated nested Laplace approximation.