Bayesian approaches for Poisson models to estimate bivariate relative risks

Initially, this work presents a review of the most common bivariate models found in the literature, with applications focused on estimating relative risks taking into account the geography effect ([1]; [2]). Additionally, a joint modeling process assuming a bivariate Poisson distribution is considered, that is, directly in the first stage of the model hierarchy. Random effects are included in the covariance or correlation parameter to control the effect of the geography. Bayesian estimation and the interpretation of the parameters of interest is discussed. The models are compared and illustrated using areal real mortality data in Chile.