Conditionally specified Gaussian Markov random field (GMRF) models with adjacency-based neighbourhood weight matrix, commonly known as neighbourhood-based GMRF models, have been the mainstream approach to spatial smoothing in Bayesian disease mapping. In the present paper, we propose a conditionally specified Gaussian random field (GRF) model with a similarity-based non-spatial weight matrix to facilitate non-spatial smoothing in Bayesian disease mapping. The model, named similarity-based GRF, is motivated for modelling disease mapping data in situations where the underlying small area relative risks and the associated determinant factors do not vary systematically in space, and the similarity is defined by similarity with respect to the associated disease determinant factors. The neighbourhood-based GMRF and the similarity-based GRF are compared and accessed via a simulation study and by two case studies, using new data on alcohol abuse in Portugal collected by the World Mental Health Survey Initiative and the well-known lip cancer data in Scotland. In the presence of disease data with no evidence of positive spatial correlation, the 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. This new approach broadens the scope of the existing conditional autocorrelation models.

Original languageEnglish
Pages (from-to)1166-1184
Number of pages19
JournalStatistical Methods In Medical Research
Issue number4
Publication statusPublished - Aug 2016
EventGEOMED Bi-Annual Meeting - Florence, Italy
Duration: 1 Sept 2015 → …


  • Neighbourhood matrix
  • Gaussian Markov random field and Gaussian random field models
  • similarity-based smoothing
  • Besag-York-Mollie model
  • disease mapping
  • alcohol abuse disorder


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