Bayesian Mapping of Medical Data - Modern Trends in Cartography - page 482

Table 3 again summarizes the statistical characteristics of the computed relative
risk rates. Globally smoothed values evince mostly the lowest characteristics and
also variability, which is clearly visible in the middle part of Fig. 2 , while the
highest statistical characteristics and variability is found in the case of the original
relative risk. The advantage of relative risk smoothing is that areas without any
recorded cases are preserved as no-risk areas. On the other hand, local differences
between methods indicate only limited usability of smoothing in this particular
study.

Identification of Clusters

Although it is possible to identify clusters of more affected or vulnerable areas from
a choropleth map, it is usually suitable to describe these clusters and quantify them.
Moran s I is probably the most widely used method for both global and local

analyses of spatial autocorrelation, i.e. estimation of spatial clustering. We men-
tioned that the eastern part of the Czech Republic (with the core of the cluster in the
north-east) is probably more affected than the western part. Upper part of Fig. 3
shows that this situation is in fact true, except for several areas in Bohemia (Prague,
Pilsen, etc.). The red in the maps stands for clusters of high values (high number of
cases), the blue stands for clusters of low values, and pink and light blue areas are
outliers. However, the first computation of local Moran

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s I is based purely on the
number of recorded cases so the analysis is distorted by the population density in all
districts.
Lower part of Fig. 3 shows the results of a similar analysis but it is different from
the previous one. One can see the changed structure of clusters and the greater
number of occurring outliers. This analysis is also based on the recorded number of
disease cases but is enhanced by the usage of population density and empirical
Bayesian rate with permutations. North-eastern Moravia and part of Silesia is still
involved in the cluster of high values but this time the cluster is significantly
smaller. Other affected districts also cluster into rather small groups that do not
cover large areas.

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Fig. 2 (continued) empirical Bayesian estimates of the relative risk based on binomial distribution
( middle ); Relative risk of campylobacteriosis in population in municipal districts in the Czech
Republic between 2008 and 2012, which is obtained by local empirical Bayesian estimates of the
relative risk based on the first order queen contiguity ( bottom )