A weighted non-connectivity penalty for detection and inference of irregularly shaped clusters.

Abstract

Methods for the detection and inference of irregularly shaped geographic clusters with count data are important tools in disease surveillance and epidemiology. Recently, several methods were developed which combine Kulldorff’s Spatial Scan Statistic with some penalty function to control the excessive freedom of shape of spatial clusters. Different penalty functions were conceived based on the cluster geometric shape or on the adjacency structure and non-connectivity of the cluster associated graph. Those penalty function were also implemented using the framework of multi-objective optimization methods. In particular, the non-connectivity penalty was shown to be very effective in cluster detection. Basically, the non-connectivity penalty function relies on the adjacency structure of the cluster’s associated graph but it does not take into account the population distribution within the cluster. Here we introduce a modification of the non-connectivity penalty function, introducing weights in the components of the penalty function according to the cluster population distribution. Our methods is able to identify multiple clusters in the study area. We show through numerical simulations that our weighted non-connectivity penalty function outperforms the original non-connectivity function in terms of power of detection, sensitivity and positive predictive value, also being computationally fast. Both single-objective and multi-objective versions of the algorithm are implemented and compared.