Abstract
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.
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Notes
Estimating with Confidence—Mid-1991 population estimates for small areas. Population Trends 1995; 82:6.
Smoking prevalence in a full probability model has one likelihood contribution from the observed smoking data and another likelihood contribution from the observed heart disease data. The cut function in WinBUGS enables the integrated model to disregard the likelihood contribution from the heart disease outcomes when constructing the full conditional distribution for the smoking prevalence. As a result, the integrated model allows for uncertainty in the smoking prevalence estimates without allowing the heart disease outcomes to influence the smoking prevalence estimates.
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Acknowledgements
The research for this paper was supported by grants from the NHS Executive Trent Research Scheme and from the University of Cambridge. The authors wish to thank three anonymous referees and the editors for their helpful comments and advice.
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Haining, R., Law, J., Maheswaran, R. et al. 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. Stoch Environ Res Risk Assess 21, 501–509 (2007). https://doi.org/10.1007/s00477-007-0134-1
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DOI: https://doi.org/10.1007/s00477-007-0134-1