Analysis of recurrent event data with spatial random effects using a Bayesian approach

Recurrent event data, which represent the occurrence of repeated incidences, are common in observational studies. Furthermore, collecting possible spatial correlations in health and environmental data is likely to provide more information for risk prediction. This article proposes a comprehensive proportional intensity model considering spatial random effects for recurrent event data using a Bayesian approach. The spatial information for areal data (where the spatial location is known up to a geographic unit such as a county) and georeferenced data (where the location is exactly observed) is examined. A traditional constant baseline intensity function, as well as a flexible piecewise constant baseline intensity function, are both under consideration. To estimate the parameters, a Markov chain Monte Carlo method with the Metropolis-Hastings algorithm and the adaptive Metropolis algorithm are applied. To assess the performance of model fitting, the deviance information criterion and log pseudo marginal likelihood are proposed. Overall, simulation studies demonstrate that the proposed model is significantly better than models that do not consider spatial effects if spatial correlations exist. Finally, our approach is implemented using a dataset related to the recurrence of cardiovascular diseases, which incorporates spatial information.