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Bayesian mapping of disease. (English) Zbl 0849.62060
Gilks, W. R. (ed.) et al., Markov chain Monte Carlo in practice. London: Chapman & Hall. 359-379 (1996).
The analysis of geographical variation in rates of disease incidence or mortality is useful in the formulation and validation of aetiological hypotheses. Disease mapping aims to elucidate the geographical distribution of underlying disease rates, and to identify areas with low or high rates. The two main conventional approaches are maps of standardized rates based on Poisson inference, and maps of statistical significance. The former has the advantage of providing estimates of the parameters of interest, the disease rates, but raises two problems.
First, for rare diseases and for small areas, variation in the observed number of events exceeds that expected from Poisson inference. In a given area, variation in the observed number of events is due partly to Poisson sampling, but also to extra-Poisson variation arising from variability in the disease rate within the area, which results from heterogeneity in individual risk levels within the area.
These considerations have led several authors to develop Bayesian approaches to disease mapping. This consists of considering, in addition to the observed events in each area, prior information on the variability of disease rates in the overall map. Bayesian estimates of area-specific disease rates integrate these two types of information.
The second problem in using the conventional approach based on Poisson inference, is that it does not take account of any spatial pattern in disease, i.e. the tendency for geographically close areas to have similar disease rates. Prior information on the rates, allowing for local geographical dependence, is pertinent. With this prior information, a Bayesian estimate of the rate in an area is shrunk towards a local mean, according to the rates in the neighbouring areas.
Empirical Bayes methods yield acceptable point estimates of the rates but underestimate their uncertainty. A direct fully Bayesian approach is rarely tractable with the non-conjugate distributions typically involved. However, Gibbs sampling has been used to simulate posterior distributions and produce satisfactory point and interval estimates for disease rates.
For the entire collection see [Zbl 0832.00018].

##### MSC:
 62P10 Applications of statistics to biology and medical sciences; meta analysis 62F15 Bayesian inference