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In recent years, spatial and spatio-temporal modeling have become animportant area of research in many fields (epidemiology, environmental studies,disease mapping). In this work we propose different spatial models to studyhospital recruitment, including some potentially explicative variables.Interest is on the distribution per geographical unit of the ratio between thenumber of patients living in this geographical unit and the population in thesame unit. Models considered are within the framework of Bayesian LatentGaussian models. Our response variable is assumed to follow a binomialdistribution, with logit link, whose parameters are the population in thegeographical unit and the corresponding relative risk. The structured additivepredictor accounts for effects of various covariates in an additive way,including smoothing functions of the covariates (for example spatial effect),linear effect of covariates. To approximate posterior marginals, which notavailable in closed form, we use integrated nested Laplace approximations(INLA), recently proposed for approximate Bayesian inference in latent Gaussianmodels. INLA has the advantage of giving very accurate approximations and beingfaster than McMC methods when the number of parameters does not exceed 6 (as itis in our case). Model comparisons are assessed using DIC criterion.

Using Integrated Nested Laplace Approximation for Modeling Spatial Healthcare Utilization