Conclusion
We have quantified to what extent some usual and some more recently developed Bayesian disease-mapping models are conservative, in the sense that they have low sensitivity for detecting raised-risk areas that have only a small excess risk but that, conversely, any identified patterns of elevated risk are, on the whole, specific. We would view this amount of conservatism as a positive feature, as we wish to avoid false alarms when investigating spatial variation in disease risk. However, the magnitude of the risk in any areas identified as raised is likely to be considerably underestimated, and it is worth investigating a range of spatial priors that produce different amounts of smoothing. Given that most environmental risks are small, it is clear that such methods are seriously underpowered to detect them. This represents a major limitation of the small-area disease-mapping approach, although exploiting the full posterior distribution of the relative risk estimates using the decision rules proposed here can improve the discrimination between areas with background and elevated rates. For localized excesses where the geographic source of the risk can be hypothesized, these methods are not appropriate, and focused tests should be used instead. Future applications of small-area disease-mapping methods should therefore consider carefully the tradeoff between size of the areas, size of the expected counts, and the anticipated magnitude and spatial structure of the putative risks. Recently proposed multivariate extensions of Bayesian disease-mapping models (e.g., Gelfand and Vounatsou 2003; Knorr-Held and Best 2001) also deserve further consideration, as they may lead to improved power by enabling risk estimates to borrow information across multiple diseases that share similar etiologies as well as across areas.