Anderson Ribeiro Duarte

Internal cohesion and geometric shape of spatial clusters

The geographic delineation of irregularly shaped spatial clusters is an ill defined problem. Whenever the spatial scan statistic is used, some kind of penalty correction needs to be used to avoid clusters’ excessive irregularity and consequent reduction of power of detection. Geometric compactness and non-connectivity regularity functions have been recently proposed as corrections. We present a novel internal cohesion regularity function based on the graph topology to penalize the presence of weak links in candidate clusters. Weak links are defined as relatively unpopulated regions within a cluster, such that their removal disconnects it. By applying this weak link cohesion function, the most geographically meaningful clusters are sifted through the immense set of possible irregularly shaped candidate cluster solutions. A multi-objective genetic algorithm (MGA) has been proposed recently to compute the Pareto-sets of clusters solutions, employing Kulldorff’s spatial scan statistic and the geometric correction as objective functions. We propose novel MGAs to maximize the spatial scan, the cohesion function and the geometric function, or combinations of these functions. Numerical tests show that our proposed MGAs has high power to detect elongated clusters, and present good sensitivity and positive predictive value. The statistical significance of the clusters in the Pareto-set are estimated through Monte Carlo simulations. Our method distinguishes clearly those geographically inadequate clusters which are worse from both geometric and internal cohesion viewpoints. Besides, a certain degree of irregularity of shape is allowed provided that it does not impact internal cohesion. Our method has better power of detection for clusters satisfying those requirements. We propose a more robust definition of spatial cluster using these concepts.

Data-driven inference for the spatial scan statistic

BackgroundKulldorffs spatial scan statistic for aggregated area maps searches for clusters of cases without specifying their size (number of areas) or geographic location in advance. Their statistical significance is tested while adjusting for the multiple testing inherent in such a procedure. However, as is shown in this work, this adjustment is not done in an even manner for all possible cluster sizes.ResultsA modification is proposed to the usual inference test of the spatial scan statistic, incorporating additional information about the size of the most likely cluster found. A new interpretation of the results of the spatial scan statistic is done, posing a modified inference question: what is the probability that the null hypothesis is rejected for the original observed cases map with a most likely cluster of size k, taking into account only those most likely clusters of size k found under null hypothesis for comparison? This question is especially important when the p-value computed by the usual inference process is near the alpha significance level, regarding the correctness of the decision based in this inference.ConclusionsA practical procedure is provided to make more accurate inferences about the most likely cluster found by the spatial scan statistic.

Adjusted Inference for the Spatial Scan Statistic

A modification is proposed to the usual inference test of the Kulldorff’s spatial scan statistic, incorporating additional information about the size of the most likely cluster found. A new modified inference question is answered: what is the probability that the null hypothesis is rejected for the original observed cases map with a most likely cluster of size known, taking into account only those most likely clusters of same size found under null hypothesis? A practical procedure is provided to make more accurate inferences about the most likely cluster found by the spatial scan statistic.

Um Algoritmo Enxame de Partículas Binário para Detecção de Clusters Irregulares

Gladston Moreira Departamento de Computação Universidade Federal de Ouro Preto Ouro Preto, Brasil 35400-000 Email: gladston@iceb.ufop.br Anderson Duarte Departamento de Estatı́stica Universidade Federal de Ouro Preto Ouro Preto, Brasil 35400-000 Email: duarte.andersonr@gmail.com David Menotti Departamento de Computação Universidade Federal de Ouro Preto Ouro Preto, Brasil 35400-000 Email: menottid@gmail.com