Modelling spatial hospital recruitment via integrated nested Laplace approximations

We propose different spatial models to study hospital recruitment, including some potentially explicative variables. Data analysed concern the hospital recruitment of the Haute Alsace a region in the north-east of France. Spatial models can be employed to show current patterns of healthcare utilization and to monitor changes in primary care access. Interest is on the distribution per geographical unit of the ratio between the number of patients living in this geographical unit and the population in the same unit. Models considered are within the framework of Bayesian latent Gaussian models. We assume that our response variable, the number of patients, follows, independently, a binomial distribution, with logit link, whose parameters are the population in each geographical unit and the corresponding risk. A flexible geoaddittive predictor is considered. To approximate posterior marginals, we use integrated nested Laplace approximations (INLA), recently proposed for approximate Bayesian inference in latent Gaussian models. Model comparisons are assessed using Deviance Information Criterion.