Using integrated nested Laplace approximations for modelling spatial healthcare utilization

In this work we propose different spatial models to study hospital recruitment, including some potentially explanatory variables. Interest is on the distribution over geographical units 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. Our response variable is assumed to follow a binomial distribution, with logit link, whose parameters are the population in the geographical unit and the corresponding risk. The structured additive predictor accounts for effects of various covariates in an additive way, including smoothing functions of the covariates (for example a spatial effect). To approximate posterior marginals, which are not available in closed form, we use integrated nested Laplace approximations (INLA), recently proposed for approximate Bayesian inference in latent Gaussian models. INLA has the advantage of giving very accurate approximations and being faster than MCMC methods when the number of hyperparameters does not exceed 6 (as in our case). Model comparison is performed using the DIC criterion.