Geographic Delineation of Disease Clusters through Multi-Objective Optimization

Irregularly shaped spatial disease clusters occur commonly in epidemiological studies, but their geographic delineation is poorly defined. Most current spatial scan software usually displays only one of the many possible cluster solutions with different shapes, from the most compact round cluster to the most irregularly shaped one, corresponding to varying degrees of penalization parameters imposed to the freedom of shape. Even when a fairly complete set of solutions is available, the choice of the most appropriate parameter setting is left to the practitioner, whose decision is often subjective. We propose quantitative criteria for choosing the best cluster solution, through multi-objective optimization, by finding the Pareto-set in the solution space. Two competing objectives are involved in the search: regularity of shape, and scan statistic value. Instead of running sequentially a cluster finding algorithm with varying degrees of penalization, the complete set of solutions is found in parallel, employing a genetic algorithm. The cluster significance concept is extended for this set in a natural and unbiased way, being employed as a decision criterion for choosing the optimal solution. The Gumbel distribution is used to approximate the empiric scan statistic distribution, speeding up the significance estimation. The method is fast, with good power of detection. An application to breast cancer clusters is discussed.