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Duczmal Luiz

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

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.

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Submitted by uysz on

Scan statistics are highly successful for the evaluation of space-time clusters. Recently, concepts from the graph theory were applied to evaluate the set of potential clusters. Wieland et al. introduced a graph theoretical method for detecting arbitrarily shaped clusters on the basis of the Euclidean minimum spanning tree of cartogram transformed case locations, which is quite effective, but the cartogram construction step of this algorithm is computationally expensive and complicated.

 

Objective

We describe a method for prospective space-time cluster detection of point event data based on the scan statistic. Our aim is to detect as early as possible the appearance of an emerging cluster of syndromic individuals because of a real outbreak of disease amidst the heterogeneous population at risk.

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Submitted by hparton 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.

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Submitted by elamb on

Ordering-based approaches [1,2] and quadtrees [3] have been introduced recently to detect multiple spatial clusters in point event datasets. The Autonomous Leaves Graph (ALG) [4] is an efficient graph-based data structure to handle the communication of cells in discrete domains. This adaptive data structure was favorably compared to common tree-based data structures (quad-trees). An additional feature of the ALG data structure is the total ordering of the component cells through a modified adaptive Hilbert curve, which links sequentially the cells (the orange curve in the example of Figure 1).

Objective

To detect multiple significant spatial clusters of disease in case-control point event data using the Autonomous Leaves Graph and the spatial scan statistic.

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Submitted by elamb on

Data obtained through public health surveillance systems are used to detect and locate clusters of cases of diseases in space-time, which may indicate the occurrence of an outbreak or an epidemic. We present a methodology based on adaptive likelihood ratios to compare the null hypothesis (no outbreaks) against the alternative hypothesis (presence of an emerging disease cluster).

 

Objective

Disease surveillance is based on methodologies to detect outbreaks as soon as possible, given an acceptable false alarm rate. We present an adaptive likelihood ratio method based on the properties of the martingale structure which allows the determination of an upper limit for the false alarm rate.

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Submitted by elamb on

The spatial scan statistic [1] is the most used measure for cluster strenght. The evaluation of all possible subsets of regions in a large dataset is computationally infeasible. Many heuristics have appeared recently to compute approximate values that maximizes the logarithm of the likelihood ratio. The Fast Subset Scan [2] finds exactly the optimal irregularly spatial cluster; however, the solution may not be connected. The spatial cluster detection problem was formulated as the classic knapsack problem [3], and modeled as a bi-objective unconstrained combinatorial optimization problem. Dynamic programming relies on the principle that, in an optimal sequence of decisions or choices, each sub-sequence must also be optimal. During the search for a solution it avoids full enumeration by pruning early partial decision solutions that cannot possibly lead to optimal solutions.

Objective

We propose a fast, exact algorithm to make detection and inference of arbitrarily shaped connected spatial clusters in aggregated area maps based on constrained dynamic programming.

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Submitted by elamb 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

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.

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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
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