Exploratory disease mapping: kriging the spatial risk function from regional count data

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Abstract
There is considerable interest in the literature on disease mapping to interpolate estimates of disease occurrence or risk of disease from a regional database onto a continuous surface. In addition to many interpolation techniques available the geostatistical method of kriging has been used but also criticised. To circumvent these critics one may use kriging along with already smoothed regional estimates, where smoothing is based on empirical Bayes estimates, also known as shrinkage estimates. The empirical Bayes step has the advantage of shrinking the unstable and often extreme estimates to the global or local mean, and also has a stabilising effect on variance by borrowing strength, as well. Negative interpolates are prevented by choice of the appropriate kriging method. The proposed mapping method is applied to the North Carolina SIDS data example as well as to an example data set from veterinary epidemiology. The SIDS data are modelled without spatial trend. And spatial interpolation is based on ordinary kriging. The second example is included to demonstrate the method when the phenomenon under study exhibits a spatial trend and interpolation is based on universal kriging. Interpolation of the regional estimates overcomes the areal bias problem and the resulting isopleth maps are easier to read than choropleth maps. The empirical Bayesian estimate for smoothing is related to internal standardization in epidemiology. Therefore, the proposed concept is easily communicable to map users.