It is often appropriate to ask questions related to the local properties of the relative risk surface rather than models of relative risk per se. Local properties of the surface could include peaks of risk, sharp boundaries between areas of risk, or local heterogeneities in risk. These diﬀerent features relate to surface properties, but not directly to a value at a speciﬁc location. Relative risk estimation (disease mapping; Chapters 6 and 7) concerns
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the “global” smoothing of risk and estimation of true underlying risk level (height of the risk surface), whereas cluster detection is focused on local features of the risk surface where elevations of risk or depressions of risk occur. Hence, it is clear that cluster detection is fundamentally diﬀerent from relative risk estimation in its focus. However, the diﬀerence can become blurred, as methods that are used for risk estimation can be extended to allow certain types of cluster detection. This will be discussed in detail in later sections. While Chapters 3, 8, and 9 deal with clustering issues and related testing, this chapter focuses solely on cluster modeling and methods related to modeling. A general review of clustering in a nonspatial and a spatial context can be found in Xu and Wunsch (2009).