Border analysis for spatial clusters

Fernando L. P. Oliveira, André L. F. Cançado, Gustavo de Souza, Gladston J. P. Moreira, Martin Kulldorff

The spatial scan statistic is widely used by public health professionals in the detection of spatial clusters in inhomogeneous point process. The most popular version of the spatial scan statistic uses a circular-shaped scanning window. Several other variants, using other parametric or non-parametric shapes, are also available. However, none of them offer information about the uncertainty on the borders of the detected clusters. We propose a new method to evaluate uncertainty on the boundaries of spatial clusters identified through the spatial scan statistic for Poisson data. For each spatial data location i, a function F(i) is calculated. While not a probability, this function takes values in the [0, 1] interval, with a higher value indicating more evidence that the location belongs to the true cluster. Through a set of simulation studies, we show that the F function provides a way to define, measure and visualize the certainty or uncertainty of each specific location belonging to the true cluster. The method can be applied whether there are one or multiple detected clusters on the map. We illustrate the new method on a data set concerning Chagas disease in Minas Gerais, Brazil. The higher the intensity given to an area, the higher the plausibility of that particular area to belong to the true cluster in case it exists. This way, the F function provides information from which the public health practitioner can perform a border analysis of the detected spatial scan statistic clusters. We have implemented and illustrated the border analysis F function in the context of the circular spatial scan statistic for spatially aggregated Poisson data. The definition is clearly independent of both the shape of the scanning window and the probability model under which the data is generated. To make the new method widely available to users, it has been implemented in the freely available SaTScan[Formula: see text] software www.satscan.org .