Three spatial patterns for areas of elevated risk were chosen. The choice of patterns was intended to span a spectrum ranging from a scenario with single isolated areas with elevated risks (the hardest test case for any smoothing method) to a scenario with a number of larger clusters of several contiguous areas with elevated risks (a situation with a substantial amount of heterogeneity). In all cases the elevated areas were selected in turn at random from the set of areas with the required expected counts. In the Simu 1 and Simu 3 cases, once an area was selected, a buffer of neighboring areas with background risk (excluded thereafter from the random selection) was placed around it to produce the required pattern of isolated high-risk clusters. The three generated patterns were defined as follows: