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Department of Geography


Bayesian modelling of environmental risk: example using a small area ecological study of coronary heart disease mortality in relation to modelled outdoor nitrogen oxide levels.

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


Bayesian modelling of health risks in relation to environmental exposures offers advantages over conventional (non-Bayesian) modelling approaches. We report an example using research into whether, after controlling for different confounders, air pollution (NOx) has a significant effect on coronary heart disease mortality, estimating the relative risk associated with different levels of exposure. We use small area data from Sheffield, England and describe how the data were assembled. We compare the results obtained using a generalized (Poisson) log-linear model with adjustment for overdispersion, with the results obtained using a hierarchical (Poisson) log-linear model with spatial random effects. Both classes of models were fitted using a Bayesian approach. Including spatial random effects models both overdispersion and spatial autocorrelation effects arising as a result of analysing data from small contiguous areas. The first modelling framework has been widely used, while the second provides a more rigorous model for hypothesis testing and risk estimation when data refer to small areas. When the models are fitted controlling only for the age and sex of the populations, the generalized log-linear model shows NOx effects are significant at all levels, whereas the hierarchical log-linear model with spatial random effects shows significant effects only at higher levels. We then adjust for deprivation and smoking prevalence. Uncertainty in the estimates of smoking prevalence, arising because the data are based on samples, was accounted for through errors-in-variables modelling. NOx effects apparently are significant at the two highest levels according to both modelling frameworks.


bayeenvironment modify fig 1

Figure 1: Map decomposition of the relative risks. Top left shows the map of ri obtained from the final model. Three decomposed components are shown. Top right: exp[f4Z4], the 4th quintile (mean value=55.8ug/m3) of NOx. Bottom left: exp[f5Z5],the 5th quintile (mean value=61.9ug/m3) of NOx. , Bottom right: the unstructured random effects, exp[U]. The maps are obtained after adjusting for deprivation and are based on posterior means.

bayeenvironment modify fig 2

Figure 2: Maps of excess relative risks of coronary heart disease of the final model. An area i is considered to have excess relative risk when 97.5% of the simulated values of relative risk of area i (ri) are greater than 1.

Further reading

Haining, R.P, J. Law, Maheswaran, R., T. Pearson, and P. Brindley (2006). “Bayesian Modelling of Environmental Risk: a Small Area Ecological Study of Coronary Heart Disease Mortality in relation to Modelled Outdoor Nitrogen Oxide Levels.” Stochastic Environmental Research and Risk Assessment (in press).