Revisiting Gaussian Markov random fields and Bayesian disease mapping.

Area of Science:

• Spatial statistics
• Biostatistics
• Epidemiology

Background:

• Gaussian Markov random fields are crucial for spatial modeling in disease mapping.
• Several models exist, including intrinsic and proper conditional autoregressive models, Leroux et al. model, and Besag, York and Mollie (BYM) model variants.
• Understanding their distinct properties is key for accurate spatial risk assessment.

Purpose of the Study:

• To critically evaluate and compare various Gaussian Markov random field models for Bayesian disease mapping.
• To analyze their performance in characterizing spatial dependencies, local influences, and covariance structures.
• To assess their utility in facilitating stabilized and efficient posterior risk prediction and inference.

Main Methods:

• Analytical and simulation studies were conducted.
• Graphic visualizations were employed for insights.
• Disease mapping case studies were utilized for practical evaluation.

Main Results:

• The intrinsic conditional autoregressive, proper conditional autoregressive, Leroux et al., and BYM models exhibit distinct spatial dependence characteristics.
• These models differ in their ability to capture local influences and spatial covariance/correlation functions.
• All evaluated models demonstrated potential for stabilized and efficient posterior risk prediction.

Conclusions:

• Gaussian Markov random fields, including conditional autoregressive and convolution models, are versatile tools in Bayesian disease mapping.
• Each model possesses unique strengths in defining spatial relationships and influences.
• These models can serve complementary roles, offering flexibility and enhancing the accuracy of spatial risk analysis.