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      Interpreting Posterior Relative Risk Estimates in Disease-Mapping Studies


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          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.

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          In the past decade conditional autoregressive modelling specifications have found considerable application for the analysis of spatial data. Nearly all of this work is done in the univariate case and employs an improper specification. Our contribution here is to move to multivariate conditional autoregressive models and to provide rich, flexible classes which yield proper distributions. Our approach is to introduce spatial autoregression parameters. We first clarify what classes can be developed from the family of Mardia (1988) and contrast with recent work of Kim et al. (2000). We then present a novel parametric linear transformation which provides an extension with attractive interpretation. We propose to employ these models as specifications for second-stage spatial effects in hierarchical models. Two applications are discussed; one for the two-dimensional case modelling spatial patterns of child growth, the other for a four-dimensional situation modelling spatial variation in HLA-B allele frequencies. In each case, full Bayesian inference is carried out using Markov chain Monte Carlo simulation.
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            Spatial correlation in ecological analysis.

            This paper presents a statistical approach, originally developed for mapping disease risk, to ecological regression analysis in the presence of spatial autocorrelated extra-Poisson variation. An insight into the effect of allowing for spatial autocorrelation on the relationship between disease rates and explanatory variables is given. Examples based on cancer frequency in Scotland and Sardinia are used to illustrate the interpretation of regression coefficient and further methodological issues.
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              A shared component model for detecting joint and selective clustering of two diseases


                Author and article information

                Environ Health Perspect
                Environmental Health Perspectives
                National Institue of Environmental Health Sciences
                June 2004
                15 April 2004
                : 112
                : 9
                : 1016-1025
                Small Area Health Statistics Unit, Department of Epidemiology and Public Health, Imperial College Faculty of Medicine, Imperial College London, Norfolk Place, London, United Kingdom
                Author notes
                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.

                This is an Open Access article: verbatim copying and redistribution of this article are permitted in all media for any purpose, provided this notice is preserved along with the article's original DOI.
                Mini-Monograph: Information Systems

                Public health
                small-area studies,specificity,environmental epidemiology,spatial smoothing,sensitivity,bayesian hierarchical models,cancer mapping


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