Detecção de clusters espacias via algoritmo scan multi-objetivo

Abstract

Situations where a disease cluster does not have a regular shape are fairly common. Moreover, maps with multiple clustering, when there is not a clearly dominating primary cluster, also occur frequently. We would like to develop a method to analyze more thoroughly the severallevels of clustering that arise naturally in a disease map divided into m regions.The spatial scan statistic is the usual measure of strength of a cluster. Another important measure is its geometric regularity. A genetic multi-objective algorithm was developed elsewhere to identify irregularly shaped clusters. That method conducts a search aiming to maximize twoobjectives, namely the scan statistic and the regularity of shape (the compactness concept). The solution presented is a Pareto-set, consisting of all the clusters found which are not worse in bothobjectives simultaneously. The significance evaluation is conducted in parallel for all the clusters in the Pareto-set through a Monte Carlo simulation. This procedure determines the best cluster solution.Instead of using a genetic algorithm, we designed a novel method that incorporated the simplicity of the circular scan, being able to detect and evaluate irregularly shaped clusters. We define the circular occupation (CO) of a cluster candidate roughly as its population divided by thepopulation inside the smallest circle containing it. The CO concept, being computationally faster, and relying on familiar concepts, is easier to grasp and substitutes here the compactness concept as another measure of regularity of shape. The scan statistic is evaluated for each of the m regions of the map taken individually. The regions are ranked accordingly in decreasing order. Let R(k) be the set containing the first k regions. A multi-objective modification of the circular scan algorithm [8] issuccessively applied for each set R(k). For each circle, the candidate cluster consists of the regions belonging to R(k) within it, and the quotient in the CO calculation takes into account all the regions of the original map inside the circle. In practice we choose only some few k values such asm,m/2,m/4,,1. For each value of k we build the Pareto-set P(k). We display all the Pareto-sets in a graph and after joining all of them we compute the global Pareto-set P(0). A Monte Carlo procedureis used for significance evaluation.The presence of knees in the Pareto-sets indicates sudden transitions in the clusters structure, corresponding to rearrangements due to the coalescence of loosely knitted (usually disconnected) clusters. Each Pareto-set contains the most likely clusters within a certain level ofgeographical information. They are related, reflecting the distribution of cases, populations and neighborhood structure of the map. Computationally, the method is only a few times slower thanthe usual circular scan.The multi-objective circular scan allows peering into the clustering structure of a map. The comparison of Pareto-sets for observed cases with those computed under null-hypothesis provides valuable hints for the spatial occurrence of diseases. The potential for monitoring incipientclusters at several geographic scales simultaneously makes this a promising tool in syndromic surveillance, especially for contagious diseases when there is a mix of short and long range spatialinteractions.