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Duarte Anderson

Heuristics to detect irregularly shaped spatial clusters were reviewed recently. The spatial scan statistic is a widely used measure of the strength of clusters. However, other measures may also be useful, such as the geometric compactness penalty, the non-connectivity penalty and other measures based on graph topology and weak links.5,6 Those penalties p(z) are often coupled with the spatial scan statistic T(z), employing either the multiplicative formula maximization maxz T(z) ! p(z) or a multiobjective optimization procedure maxz(T(z), p(z)),3,6 or even a combination of both approaches. The geometric penalty of a cluster z is defined as the quotient of the area of z by the area of the circle, with the same perimeter as the convex hull of z, thus penalizing more the less rounded clusters. Now, let V and E be the vertices and edges sets, respectively, of the graph Gz(V, E) associated with the potential cluster z. The non-connectivity penalty y(z) is a function of the number of edges e(z) and the number of nodes n(z) of Gz(V, E), defined as y(z) ¼ e(z)/3[n(z)#2]. The less interconnected tree-shaped clusters are the most penalized. However, none of those two measures includes the effect of the individual populations.

Objective

Irregularly shaped clusters in maps divided into regions are very common in disease surveillance. However, they are difficult to delineate, and usually we notice a loss of power of detection. Several penalty measures for the excessive freedom of shape have been proposed to attack this problem, involving the geometry and graph topology of clusters. We present a novel topological measure that displays better performance in numerical tests.

Referenced File
Submitted by uysz on

Spatial cluster analysis is considered an important technique for the elucidation of disease causes and epidemiological surveillance. Kulldorff's spatial scan statistic, defined as a likelihood ratio, is the usual measure of the strength of geographic clusters. The circular scan, a particular case of the spatial scan statistic, is currently the most used tool for the detection and inference of spatial clusters of disease.

Kulldorff's 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. We propose a modification to the usual inference test of the spatial scan statistic, incorporating additional information about the size of the most likely cluster found.

 

Objective

We propose a modification to the usual inference test of the spatial scan statistic, incorporating additional information about the size of the most likely cluster found.

Referenced File
Submitted by elamb on

The Voronoi Based Scan (VBScan)[1] is a fast method for the detection and inference of point data set space-time disease clusters. 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 Minimum Spanning Tree (MST) linking the cases. The successive removal of its edges generates sub-trees which are the potential space-time clusters, which are evaluated through the scan statistic [2]. Monte Carlo replications of the original data are used to evaluate cluster significance. In the present work we modify VBScan to find the best partition dividing the map into multiple low and high risk regions.

Objective

We describe a method to determine the partition of a map consisting of point event data, identifying all the multiple significant anomalies, which may be of high or low risk, thus monitoring the existence of possible outbreaks.

Referenced File
Submitted by elamb on

Irregularly shaped cluster finders frequently end up with a solution consisting of a large zone z spreading through the map, which is merely a collection of the highest valued regions, but not a geographically sound cluster. One way to amenize this problem is to introduce penalty functions to avoid the excessive freedom of shape of z. The compactness penalty K(z) is a function used to reduce the scan value of irregularly shaped clusters, based on its geometric shape. Another penalty is the cohesion function C(z), a measure of the absence of weak links, or underpopulated regions within the cluster which disconnect it when removed. It was mentioned in that such weak links could be responsible for a diminished power of detection in cluster finder algorithms. Methods using those penalty functions present better performance. The geometric  compactness is not entirely satisfactory, although, because it has a tendency to avoid potentially interesting irregularly shaped clusters, acting as a low-pass filter. The cohesion function penalty method, although, has slightly less specificity.

 

Objective

We introduce a novel spatial scan algorithm for finding irregularly shaped disease clusters maximizing simultaneously two objectives: the regularity of shape and the internal cohesion of the cluster.

Referenced File
Submitted by elamb on

Many heuristics were developed recently to find arbitrarily shaped clusters (see  review  [1]). The most popular statistic is the spatial scan  [2]. Nevertheless, even if all cluster solutions could be known, the problem  of selecting the best cluster is ill posed. This happens because other measures, such as geometric regularity  [3-5] or topology  [6] must be taken intoconsideration. Most cluster finding  methods does not address  this last problem. A genetic multi-objective algorithm was developed elsewhere to identify irregularlyshaped clusters [5]. That method conducts a search aiming to maximize two objectives, namely the scan  statistic and the regularity of shape (using the compactness concept).The solution presented is a Pareto-set, consisting of all the clusters found which are not simultaneously worse in both objectives. The significance evaluation is conducted in parallel for all the  clusters  in  the  Pareto-set  through a  Monte Carlo simulation, determining the best cluster solution.

Objective

Irregularly shaped clusters occur naturally in disease surveillance, but they are not well defined. The number of possible clusters increases exponentially with the number of regions in a map. This concurs to reduce the power of detection, motivating the utilization of some kind of penalty function to avoid excessive freedom of shape. We introduce a weak link based correction which penalizes inconsistent clusters, without forbidding the presence of the geographically interesting irregularly shaped ones.

Referenced File
Submitted by elamb on
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