Testing spatial cluster occurrence in maps equipped with environmentally defined structures

We propose a novel tool for testing hypotheses concerning the adequacy of environmentally defined factors for local clustering of diseases, through the comparative evaluation of the significance of the most likely clusters detected under maps whose neighborhood structures were modified according to those factors. A multi-objective genetic algorithm scan statistic is employed for finding spatial clusters in a map divided in a finite number of regions, whose adjacency is defined by a graph structure. This cluster finder maximizes two objectives, the spatial scan statistic and the regularity of cluster shape. Instead of specifying locations for the possible clusters a priori, as is currently done for cluster finders based on focused algorithms, we alter the usual adjacency induced by the common geographical boundary between regions. In our approach, the connectivity between regions is reinforced or weakened, according to certain environmental features of interest associated with the map. We build various plausible scenarios, each time modifying the adjacency structure on specific geographic areas in the map, and run the multi-objective genetic algorithm for selecting the best cluster solutions for each one of the selected scenarios. The statistical significances of the most likely clusters are estimated through Monte Carlo simulations. The clusters with the lowest estimated p-values, along with their corresponding maps of enhanced environmental features, are displayed for comparative analysis. Therefore the probability of cluster detection is increased or decreased, according to changes made in the adjacency graph structure, related to the selection of environmental features. The eventual identification of the specific environmental conditions which induce the most significant clusters enables the practitioner to accept or reject different hypotheses concerning the relevance of geographical factors. Numerical simulation studies and an application for malaria clusters in Brazil are presented.