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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.

Referenced File
Submitted by uysz on

Consider the most likely disease cluster produced by any given method, like SaTScan,  for the detection and inference of spatial clusters in a map divided into areas; if this cluster is found to be statistically significant, what could be said of the external areas adjacent to the cluster? Do we have enough information to exclude them from a health program of prevention? Do all the areas inside the cluster have the same importance from a practitioner perspective? How to access quantitatively the risk of those regions, given that the information we have (cases count) is also subject to variation in our statistical modeling? A few papers have tackled these questions recently; produces confidence intervals for the risk in every area, which are compared with the risks inside the most likely cluster. There exists a crescent demand of interactive software for the visualization of spatial clusters. A technique was developed to visualize relative risk and statistical significance simultaneously.

Objective

Given an aggregated-area map with disease cases data, we propose a criterion to measure the plausibility of each area in the map of being part of a possible localized anomaly.

Referenced File
Submitted by uysz on

The spatial scan statistic proposed by Kulldorff has been widely used in spatial disease surveillance and other spatial cluster detection applications. In one of its versions, such scan statistic was developed for inhomogeneous Poisson process. However, the underlying Poisson process may not be suitable to properly model the data. Particularly, for diseases with very low prevalence, the number of cases may be very low and zero excess may cause bias in the inferences.

Lambert introduced the zero-inflated Poisson (ZIP) regression model to account for excess zeros in counts of manufacturing defects. The use of such model has been applied to innumerous situations. Count data, like contingency tables, often contain cells having zero counts. If a given cell has a positive probability associated to it, a zero count is called a sampling zero. However, a zero for a cell in which it is theoretically impossible to have observations is called structural zero.

 

Objective

The scan statistic is widely used in spatial cluster detection applications of inhomogeneous Poisson processes. However, real data may present substantial departure from the underlying Poisson process. One of the possible departures has to do with zero excess. Some studies point out that when applied to zero-inflated data the spatial scan statistic may produce biased inferences. Particularly, Gomez-Rubio and Lopez-Quılez argue that Kulldorff’s scan statistic may not be suitable for very rare diseases problems. In this work we develop a closed-form scan statistic for cluster detection of spatial count data with zero excess.

Referenced File
Submitted by elamb on

Irregularly shaped spatial disease clusters occur commonly in epidemiological studies, but their geographic delineation is poorly defined. Most current spatial scan software usually displays only one of the many possible cluster solutions with different shapes, from the most compact round cluster to the most irregularly shaped one, corresponding to varying degrees of penalization parameters imposed to the freedom of shape. Even when a fairly complete set of solutions is available, the choice of the most appropriate parameter setting is left to the practitioner, whose decision is often subjective.

 

Objective

We propose a novel approach to the delineation of irregularly shaped disease clusters, treating it as a multi-objective optimization problem. We present a new insight into the geographic meaning of the cluster solution set, providing a quantitative approach to the problem of selecting the most appropriate solution among the many possible ones.

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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