Disease mapping models for data with weak spatial dependence or spatial discontinuities

Recent advances in the spatial epidemiology literature have extended traditional approaches by including determinant disease factors that allow for non-local smoothing and/or non-spatial smoothing. In this article, two of those approaches are compared and are further extended to areas of high interest from the public health perspective. These are a conditionally specified Gaussian random field model, using a similarity-based non-spatial weight matrix to facilitate non-spatial smoothing in Bayesian disease mapping; and a spatially adaptive conditional autoregressive prior model. The methods are specially design to handle cases when there is no evidence of positive spatial correlation or the appropriate mix between local and global smoothing is not constant across the region being study. Both approaches proposed in this article are producing results consistent with the published knowledge, and are increasing the accuracy to clearly determine areas of high- or low-risk.