Kulldorff's Spatial Scan Statistic
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Indications/Recommendations for use: Scan for clusters in space that depend on time. This method does not require a priori knowledge of the population size at elevated risk
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Description: Identifies a significant excess of cases within a moving cylindrical window that visits all spatio-temporal locations, increasing in size in both space and time until it reaches an upper size limit. The scan statistic provides a measure of how unlikely it would be to encounter the observed excess of cases in a larger comparison region.
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Test statistic: A cylindrical window is defined and moved systematically throughout the study geographic and temporal space. The window size varies, and the likelihood ratio test statistic over all possible windows is calculated, conditioning on the observed total number of cases.
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Poisson model:
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Bernoulli model:
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Null Hypothesis:
The null spatial model is any inhomogeneous Poisson or Bernoulli process whose intensity (e.g. Poisson parameter) is proportional to some known function, such as population size and risk.
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Ho:
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Alternative Hypothesis:
In some locations in the multidimensional space the number of cases exceeds that predicted under the null model.
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Ha:
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GeoMed Inputs:
Group-level data with centroid coordinate, case counts, population-at-risk size per region. Upper window size limit.
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GeoMed Outputs:
Information about most likely cluster and secondary clusters such as log likelihood ratio and p-value from Monte Carlo simulations. Mapped information provides cluster locations.
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Example Analysis
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Reference:
Kulldorff, M. 1999. Spatial scan statistics: models, calculations, and applications, in Scan Statistics and Applications. Glaz, J & Balakrishnan (eds.), Birkhauser, Boston, pp.303-322.
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