Duczmal Luiz

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.

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.

The spatial scan statistic is the usual measure of strength of a cluster [1]. Another important measure is its geometric regularity [2]. A genetic multiobjective algorithm was developed elsewhere to identify irregularly shaped clusters [3]. A search is executed 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. A significance evaluation is conducted in parallel for all clusters in the Pareto-set through Monte Carlo simulation, then finding the most likely cluster. \

Objective

Situations where a disease cluster does not have a regular shape are fairly common. Moreover, maps with multiple clustering, when there is not a clearly dominating primary cluster, also occur frequently. We would like to develop a method to analyze more thoroughly the several levels of clustering that arise naturally in a disease map divided into m regions.

Early warning systems must not always rely on geographical proximity for modeling the spread of contagious diseases. Instead, graph structures such as airways or social networks are more adequate in those situations. Nodes, associated to cities, are linked by means of edges, which represent routes between cities. Scan statistics are highly successful for the evaluation of clusters in maps based on geographical proximity. The more flexible neighborhood structure of graphs presents difficulties for the direct usage of scan statistics, due to the highly irregular structures involved. Besides, the traffic intensity between connected nodes plays a significant role which is not usually present in scan statistic based models.

Objective 

We describe a model for cluster detection and inference on networks based on the scan statistic. Our aim is to detect as early as possible the appearance of an emerging cluster of syndromes due to a real outbreak (signal) amidst unrelated syndromes (noise).

Multiple or irregularly shaped spatial clusters are often found in disease or syndromic surveillance maps. We develop a novel method to delineate the contours of spatial clusters, especially when there is not a clearly dominating primary cluster, through artificial neural networks. The method may be applied either for maps divided into regions or point data set maps.