Statistical methods for the detection of spatial clustering in case-control data.

In this paper, I develop new approaches for the detection of spatial clustering in case-control data. One method is based upon drawing Thiessen polygons around each control. It is unnecessary to actually draw or compute the boundaries of the polygons; it is sufficient to count, for each control, the number of cases that are closer to that control than to any other control. A second method is similar to the Cuzick-Edwards method, which is based on counts of cases that are among the k-nearest neighbours of cases, but is instead based upon the number of cases within a specified distance of cases. These first two methods are global methods in the sense that they provide a single statistic that measures the degree of spatial clustering. The third method suggests a local statistic, for tests of the null hypothesis of no spatial clustering around a prespecified focus. The method is based upon the cumulative chi2 test, which is typically used to test whether cases are more prevalent than expected around a prespecified location. This is also extended to the case where all observational locations are considered as potential cluster locations and multiple testing is carried out. Each of the new methods is illustrated using data on childhood leukaemia and lymphoma cases in North Humberside.