Comparing two models for disease mapping data not varying systematically in space

Conditionally specified Gaussian Markov random field (GMRF) models with adjacency- based neighborhood weight matrix, commonly known as neighborhood-based GMRF models, have been the mainstream approach to spatial smoothing in Bayesian disease mapping. However, there are 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. Two models have been proposed for those cases, a conditionally specified Gaussian random field (GRF) 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 former model, named similarity-based GRF, is motivated for modeling disease mapping data in
situations where the underlying small area relative risks and the associated determinant factors do not varying systematically in space, and the similarity is defined by similarity with respect to the associated disease determinant factors. In the presence of disease data with no evidence of positive spatial correlation, a simulation study showed a consistent gain in efficiency from the similarity-based GRF, compared with the adjacency-based GMRF with the determinant risk
factors as covariate. The latter model considers a spatially adaptive extension of Leroux et al.
(2000) prior to reflect the fact that the appropriate mix between local and global smoothing may not be constant across the region being studied. Local smoothing will not be indicated when an area is disparate from its neighbours (e.g. in terms of social or environmental risk factors for the health outcome being considered). The prior for varying spatial correlation parameters may be
based on a regression structure which includes possible observed sources of disparity between neighbours. We will compare the results of the two models using data from several sources.