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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.

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Submitted by uysz on

The intrinsic variability that exists in the cases counting data for aggregated-area maps amounts to a corresponding uncertainty in the delineation of the most likely cluster found by methods based on the spatial scan statistics [3]. If this cluster turns out to be statistically significant it allows the characterization of a possible localized anomaly, dividing the areas in the map in two classes: those inside and outside the cluster. But, what about the areas that are outside the cluster but adjacent to it, sometimes sharing a physical border with an area inside the cluster? Should we simply discard them in a disease prevention program? Do all the areas inside the detected cluster have the same priority concerning public health actions? The intensity function [2], a recently introduced visualization method, answers those questions assigning a plausibility to each area of the study map to belong to the most likely cluster detected by the scan statistics. We use the intensity function to study cases of diabetes in Minas Gerais state, Brazil.

Objective

Cluster finder tools like SaTScan[1] usually do not assess the uncertainty in the location of spatial disease clusters. Using the nonparametric intensity function[2], a recently introduced visualization method of spatial clusters, we study the occurrence of several non-contageous diseases in Minas Gerais state, in Southeast Brazil.

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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.

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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

The traditional SaTScan algorithm[1],[2] uses the euclidean dis- tance between centroids of the regions in a map to assemble a con- nected (in the sense that two connected regions share a physical border) sets of regions. According to the value of the respective log- arithm of the likelihood ratio (LLR) a connected set of regions can be classified as a statistically significant detected cluster. Considering the study of events like contagious diseases or homicides we con- sider using the flow of people between two regions in order to build up a set of regions (zone) with high incidence of cases of the event. In this sense the regions will be closer as the greater the flow of peo- ple between them. In a cluster of regions formed according to the cri- terion of proximity due to the flow of people, the regions will be not necessarily connected to each other.

 

Objective

We present a new approach to the circular scan method [1] that uses the flow of people to detect and infer clusters of regions with high incidence of some event randomly distributed in a map. We use a real database of homicides cases in Minas Gerais state, in south- east Brazil to compare our proposed method with the original circu- lar scan method in a study of simulated clusters and the real situation.

Submitted by dbedford on
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