Comparing hierarchical models for spatio-temporally misaligned data using the deviance information criterion

Area of Science:

• Biostatistics
• Spatial Epidemiology
• Geographic Information Systems

Background:

• Bayes and empirical Bayes methods are established for smoothing disease risk maps.
• Spatial misalignment and temporal changes complicate disease risk analysis.
• Hierarchical Bayesian models are computationally intensive and difficult to compare.

Purpose of the Study:

• To compare hierarchical Bayesian models for spatially misaligned and temporally evolving areal data.
• To evaluate the utility of the deviance information criterion (DIC) for model comparison in this context.
• To investigate the delta method for assessing the significance of DIC differences.

Main Methods:

• Application of hierarchical Bayesian methods using Markov chain Monte Carlo (MCMC).
• Utilized the deviance information criterion (DIC) for model comparison.
• Employed the delta method to estimate variance for DIC.

Main Results:

• The deviance information criterion (DIC) provides a method for comparing complex hierarchical models.
• The delta method can be used to assess the statistical significance of differences in DIC.
• The approach was illustrated using traffic density and paediatric asthma hospitalizations in San Diego County.

Conclusions:

• The deviance information criterion (DIC) is a valuable tool for comparing hierarchical Bayesian models with complex data structures.
• The delta method enhances the interpretability of DIC by providing significance estimates.
• This methodology is applicable to real-world epidemiological studies with spatial and temporal complexities.