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Department of Geography


Analysing the relationship between smoking and coronary heart disease at the small area level: a Bayesian approach to spatial modelling

Research Team: Jane Law, Robert Haining, Ravi Maheswaran, and Tim Pearson


We model the relationship between coronary heart disease and smoking prevalence and deprivation at the small area level using the Poisson log-linear model with and without random effects. Extra-Poisson variability (overdispersion) is handled through the addition of spatially structured and unstructured random effects in a Bayesian model. In addition four different measures of smoking prevalence are assessed because the smoking data are obtained from a survey which resulted in quite large differences in the size of the sample across the set of census tracts. Two of the methods use Bayes adjustments of standardised smoking ratios (local and global adjustments) and one uses a non-parametric spatial averaging technique. A preferred model is identified based on the Deviance Information Criterion. Both smoking and deprivation turn out to be statistically significant risk factors but the effect of the smoking variable is reduced once the confounding effects of deprivation are allowed for. Maps of the spatial variability in relative risk and the importance of the underlying covariates and random effects terms are produced. We also identify areas with excess relative risk.


smokecoronary fig 1

Figure 1: Poisson log normal model with convolution prior (spatially structured and unstructured random effects).

smokecoronary fig 2

Figure 2: Smoothing of smoking ratios.

smokecoronary fig 3

Figure 3: Map decomposition of the Bayesian results.

smokecoronary fig 4

Figure 4: Map of excess relative risks.

Further reading

Law, J., R. P. Haining, R. Maheswaran, and T. Pearson (2006). “Analysing the Relationship between Smoking and Coronary Heart Disease at the Small Area Level: A Bayesian Approach to Spatial Modelling.” Geographical Analysis 38:2 140-159.