Multi-objective dynamic programming for spatial cluster detection.

Abstract

The detection and inference of arbitrarily shaped spatial clusters in aggregated geographical areas is described here as a multi-objective combinatorial optimization problem. A multi-objective dynamic programming algorithm, the Geo Dynamic Scan, is proposed for this formulation, finding a collection of Pareto-optimal solutions. It takes into account the geographical proximity between areas, thus allowing a disconnected subset of aggregated areas to be included in the efficient solutions set. It is shown that the collection of efficient solutions generated by this approach contains all the solutions maximizing the spatial scan statistic. The plurality of the efficient solutions set is potentially useful to analyze variations of the most likely cluster and to investigate covariates. Numerical simulations are conducted to evaluate the algorithm. A study case with Chagas’ disease clusters in Brazil is presented, with covariate analysis showing strong correlation of disease occurrence with environmental data.