title: Voronoi distance based prospective space-time scans for point data sets: a dengue fever cluster analysis in a southeast Brazilian town.
abstract: BACKGROUND
  The Prospective Space-Time scan statistic (PST) is widely used for the evaluation of space-time clusters of point event data. Usually a window of cylindrical shape is employed, with a circular or elliptical base in the space domain. Recently, the concept of Minimum Spanning Tree (MST) was applied to specify the set of potential clusters, through the Density-Equalizing Euclidean MST (DEEMST) method, for the detection of arbitrarily shaped clusters. The original map is cartogram transformed, such that the control points are spread uniformly. That method is quite effective, but the cartogram construction is computationally expensive and complicated.
  
  
  RESULTS
  A fast method for the detection and inference of point data set space-time disease clusters is presented, the Voronoi Based Scan (VBScan). A Voronoi diagram is built for points representing population individuals (cases and controls). The number of Voronoi cells boundaries intercepted by the line segment joining two cases points defines the Voronoi distance between those points. That distance is used to approximate the density of the heterogeneous population and build the Voronoi distance MST linking the cases. The successive removal of edges from the Voronoi distance MST generates sub-trees which are the potential space-time clusters. Finally, those clusters are evaluated through the scan statistic. Monte Carlo replications of the original data are used to evaluate the significance of the clusters. An application for dengue fever in a small Brazilian city is presented.
  
  
  CONCLUSIONS
  The ability to promptly detect space-time clusters of disease outbreaks, when the number of individuals is large, was shown to be feasible, due to the reduced computational load of VBScan. Instead of changing the map, VBScan modifies the metric used to define the distance between cases, without requiring the cartogram construction. Numerical simulations showed that VBScan has higher power of detection, sensitivity and positive predicted value than the Elliptic PST. Furthermore, as VBScan also incorporates topological information from the point neighborhood structure, in addition to the usual geometric information, it is more robust than purely geometric methods such as the elliptic scan. Those advantages were illustrated in a real setting for dengue fever space-time clusters.
authors.affiliation: Department of Statistics, Universidade Federal de Minas Gerais, Campus Pampulha, Belo Horizonte, Brazil. duczmal@est.ufmg.br
authors.forename: Luiz H
authors.initials: LH
authors.lastname: Duczmal
authors.forename: Gladston Jp
authors.initials: GJ
authors.lastname: Moreira
authors.forename: Denise
authors.initials: D
authors.lastname: Burgarelli
authors.forename: Ricardo Hc
authors.initials: RH
authors.lastname: Takahashi
authors.forename: Flávia Co
authors.initials: FC
authors.lastname: Magalhães
authors.forename: Emerson C
authors.initials: EC
authors.lastname: Bodevan
mesh_terms: D001938:Brazil / Q000453:epidemiology; D016022:Case-Control Studies; D016000:Cluster Analysis; D003715:Dengue / Q000453:epidemiology*; D004196:Disease Outbreaks; D006297:Health Services Accessibility; D006801:Humans; D011446:Prospective Studies; D013029:Space-Time Clustering; D013223:Statistics as Topic / Q000379:methods*; D013997:Time Factors