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28 September 2007 APHEO Conference 2007 2
Outline
Clusters & Cluster Detection Spatial Scan StatisticCase Study
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What is a cluster?
An unusual collection of eventsUnusual aggregation of real or perceived health eventsA geographically and/or temporally bounded collection of occurrences:
of a disease already known to occur typically in clusters, orof sufficient size and concentration to be unlikely to have occurred by chance, orrelated to each other through some social or biological mechanism, or having a common relationship with some other event or circumstance (Knox, 1989)
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Cluster Detection
GIS can be used as a quick screening tool to identify clusters
Identification of clusters can lead to interventions, even when etiology is uncertain
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Interesting Questions to be Asked
Over what scale does any clustering occur?Are clusters merely a result of some obvious a priori heterogeneity in the study region?Are they associated with proximity to other features of interest, such as transport arteries or possible point sources of pollution?Are events that cluster in space also clustered in time?
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Global and Local Tests
Global tests detect the presence or absence of clustering over the whole study region without specifying the spatial location.Local tests additionally specify the location and if extended to consider temporal patterns, can specify spatio-temporal clusters.
A special case of local tests is the focused test which is used to detect raised incidence of disease around some pre-specified source, such as an incinerator.
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Point Based Methods
Global MeasuresRipley’s K Function (and its variants)
CrimeStat, Splus/R
Local MeasuresKernel Density Estimation
ArcGIS, CrimeStat, Splus
Kuldorff’s Spatial Scan Statistic
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Area Based Methods
Global MeasuresMoran’s I
ArcGIS, GeoDA, CrimeStat, Splus/R
Local MeasuresLocal Moran’s I
ArcGIS, GeoDa, CrimeStat, R
Kuldorff’s Spatial Scan Statistic
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Introduction to SaTScan 7.0.3
Analyzes spatial, temporal and spatio-temporal data through a scan statisticQuick assessment of potential clustersDeveloped by Martin Kuldorff for the National Cancer InstituteFreely available from www.satscan.org
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Objectives of the software (1)
To perform geographical surveillance of disease, to detect areas of significantly high or low rates
To test whether a disease is randomly distributed over space, over time or over space and time.
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To evaluate reported spatial or space-time disease clusters, to see if they are statistically significant
To perform repeated time-periodic disease surveillance for the early detection of disease outbreaks.
Objectives of the software (2)
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How does it work? (1)
A circular scanning window is placed at different coordinates with radii that vary from 0 to some set upper limit.
For each location and size of window:
HA = elevated risk within window as compared to outside of window
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How does it work? (3)
Rainy River can be the centerof 14 potential clusters
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How does it work? (4)
Likelihood function is created depending on model selected (more later…..)
Likelihood = hypothetical probability that an event that has already occurred would yield a specific outcomeFunction is maximized over all window locations and sizes
The one with the maximum likelihood is most likely cluster (least likely to have occurred by chance)Likelihood ratio for this window becomes maximum likelihood ratio test statisticA p-value is obtained for the cluster by Monte Carlo hypothesis testing
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How does it work? (5)
Indicates whether there is clusteringShows us where it is (text description)Evaluates its statistical significanceProduces a relative risk for the cluster
Which can be low or high riskSolves the Texas Sharpshooter problem --does not rely on a priori knowledge of any cluster
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Poisson models
Should be used when background population reflects a certain risk mass such as total persons in an area
Expected number of cases is directly proportional to the total number of persons
Example – # cases of cancer per 100,000 persons
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How the Poisson model works
How the scan works in this caseLikelihood function:
C = total number of casesc = observed number of cases in windowE[c] = covariate adjusted expected number of cases in windowI() = indicator function
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Output
Need to import this into ArcView forvisualization.
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Bernoulli models
Bernoulli process is a discrete-time stochastic process based on Bernoulli trials
An experiment whose outcome is random and can be either of two possible outcomes, “success” and “failure”Values expressed as 0 or 1 (non-cases or cases)
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Scan similar to Poisson, visiting each eventLikelihood function:
C = total number of cases in datasetc = observed number of cases in windown = total # of cases and controls in windowN = total number of cases and controls in dataset
How the Bernoulli model works
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Focused tests
Focused tests can be conducted by providing the coordinates of one or more point sources. In these instances, the scan will only evaluate clusters around these sources and bypass the rest of the coordinates