| Interpreting Posterior Relative Risk Estimates in Disease-Mapping Studies Sylvia Richardson, Andrew Thomson, Nicky Best, and Paul Elliott Small Area Health Statistics Unit, Department of Epidemiology and Public Health,
Imperial College Faculty of Medicine, Imperial College London, Norfolk Place,
London, United Kingdom Abstract
There is currently much interest in conducting spatial analyses of health outcomes at the small-area scale. This requires sophisticated statistical techniques, usually involving Bayesian models, to smooth the underlying risk estimates because the data are typically sparse. However, questions have been raised about the performance of these models for recovering the "true" risk surface, about the influence of the prior structure specified, and about the amount of smoothing of the risks that is actually performed. We describe a comprehensive simulation study designed to address these questions. Our results show that Bayesian disease-mapping models are essentially conservative, with high specificity even in situations with very sparse data but low sensitivity if the raised-risk areas have only a moderate (< 2-fold) excess or are not based on substantial expected counts (> 50 per area) . Semiparametric spatial mixture models typically produce less smoothing than their conditional autoregressive counterpart when there is sufficient information in the data (moderate-size expected count and/or high true excess risk) . Sensitivity may be improved by exploiting the whole posterior distribution to try to detect true raised-risk areas rather than just reporting and mapping the mean posterior relative risk. For the widely used conditional autoregressive model, we show that a decision rule based on computing the probability that the relative risk is above 1 with a cutoff between 70 and 80% gives a specific rule with reasonable sensitivity for a range of scenarios having moderate expected counts (~ 20) and excess risks (~1.5- to 2-fold) . Larger (3-fold) excess risks are detected almost certainly using this rule, even when based on small expected counts, although the mean of the posterior distribution is typically smoothed to about half the true value. Key words: Bayesian hierarchical models, cancer mapping, environmental epidemiology, sensitivity, small-area studies, spatial smoothing, specificity. Environ Health Perspect 112:1016-1025 (2004) . doi:10.1289/ehp.6740 available via http://dx.doi.org/ [Online 15 April 2004]
This aticle is part of the mini-monograph "Health and Environment Information Systems for Exposure and Disease Mapping, and Risk Assessment." Address correspondence to S. Richardson, Department of Epidemiology and Public Health, Imperial College Faculty of Medicine, Imperial College London, Norfolk Place, London, W2 1PG, United Kingdom. Telephone: 44 0 207 594 3336. Fax: 44 0 207 402 2150. E-mail: sylvia.richardson@imperial.ac.uk We thank P. Green for stimulating discussions and for providing the computer code of the MIX model. The U.K. Small Area Health Statistics Unit is funded by the Department of Health, Department of the Environment, Food and Rural Affairs, Environment Agency, Health and Safety Executive, Scottish Executive, National Assembly for Wales, and the Northern Ireland Assembly. The authors declare they have no competing financial interests. Received 12 September 2003 ; accepted 2 March 2004.
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