1. Spatial Clusters and Pattern Analysis
Chris Jochem
Geog 5161 – Spring 2011

2. When you know ‘where’, you can start to ask ‘why’
John Snow’s map of cholera deaths in London, 1854.
Need to move beyond simply mapping events and beyond general point pattern analysis.
Water pump locations

3. Goals of Cluster Analysis
Examine “unusual” groupings of events in space and/or time (Cromley and McLafferty 2002)
Both confirmatory and exploratory of hypotheses
Different ways to operationalize unusual or unexpected patterns using probability distributions
Common Questions (Waller and Gotway 2004, 155):
Do cases tend to occur near other cases? (possible infectious agent)
Does a particular area within the study region seem to contain a significant excess of observed events? (possible environmental risk factor)
Where are the most unusual collection of cases? (possible cluster)

4. Different Methodologies
… for different levels of analysis
Point Pattern Analysis: density and distance measurements
Ex: density map of cholera cases
Clustering requires different statistical tests
often used sequentially or as part of a larger study to select areas for more detailed field work.
Three main categories of tests:
Global
Local
Focal

5. 3 main Categories of Tests
Global: a single test for general patterns and spatial autocorrelation over an entire study region
Moran’s I
Geary’s C
Local: search for specific regions or areas where clustering is observed above expected levels
Example: areas of high crime or terrorist attacks
Local Moran’s I
Getis-Ord Gi*
Spatial Scan Statistic
Focal: specialized statistics searching only in regions around fixed locations
Example: cancers around nuclear reactors
Stone’s Test
Bithell
Tango

6. Consider your Data Point Data
Events (diseases crimes, conflicts, etc.)
Cases/Controls
Measurement locations
Considerations
Point level accuracy
Polygon Data
Census or social attributes (poverty, unemployment, income, etc.)
Aggregate counts of individual-level events
Considerations
Modifiable areal unit problem (MAUP)

7. Spatial Scan Statistic
As implemented in SatScan® software
Input point or area data for events and background population, can vary over time
Pass a circular or elliptical filter of varying radii across study area
Count observed cases and test likelihood ratio against expected cases given the population or person-time
Pros
Cons
Spatial, temporal, or space-time clusters
Controls for risk factors and covariates
Learning curve for set-up and interpretation
No graphical output

8. Examples
O’Loughlin, John and Frank D. W. Witmer The Localized Geographies of Violence in the North Caucasus of Russia, The Annals of the Association of American Geographers 101, no. 1 (January): 178 – 201.
Using a spatial scan statistic to find local clusters of conflicts in space and time.

9. Examples
Kulldorff M, Athas W, Feuer E, Miller B, Key C. Evaluating cluster alarms: A space-time scan statistic and brain cancer in Los Alamos. American Journal of Public Health, 1998; 88:
See the demo!
Many additional examples:

10. Considerations and Critiques
Must consider data limitations and accuracies
How do you define a ‘cluster’?  expected outcomes
Possibility of occurring by chance, especially with small numbers
Based on theory or hypothesized relationships
“Texas Sharpshooter Fallacy”

11. Considerations and Critiques
Must consider underlying population at risk
People are not evenly distributed
Complete spatial randomness is usually not valid
Difficult to link causality to clusters (Elliot et al. 2000, Elliot and Wakefield 2001)
Usually requires further studies
What matters is scientific, not statistical, significance (Gould 1970)
See also O’Sullivan and Unwin (2003), and Harvey (1966,1967)

12. Resources Free Software: SatScan: http://www.satscan.org/
CrimeStat:
GeoDa:
R packages:
Broad Street Cholera Data:

13. References
Anselin, Luc How (not) to lie with spatial statistics. American Journal of Preventive Medicine 30: s3-s6. Cromley, Ellen K. and Sara L. McLafferty GIS and Public Health. New York: Guilford Press. Elliott, Paul and Jon Wakefield Disease clusters: Should they be investigated, and, if so, when and how? Journal of the Royal Statistical Society A 164, 1: Elliott, Paul, Jon Wakefield, Nicola Best, and David Briggs Spatial Epidemiology: Methods and Applications. Oxford University Press. Gould, Peter Is statistix inferens the geographic name for a wild goose? Economic Geography 46 (June): Harvey, David W Geographical processes and the analysis of point patterns: Testing models of diffusion by quadrat sampling. Transactions of the Institute of British Geographers 40: Harvey, David W Some methodological problems in the useof Neyman type A and negative binomial distribution for the analysis of point patterns. Transactions of the Institute of British Geographers 44:

14. References
Kulldorff, Martin, and Neville Nagarwalla Spatial disease clusters: Detection and inference. Statistics in Medicine 14: Kulldorff, Martin, W. Athas, E. Feuer, B. Miller, and C. Key Evaluating cluster alarms: A space-time scan statistic and brain cancer in Los Alamos. American Journal of Public Health 88: Kulldorff, Martin A spatial scan statistic. Communications in Statistics – Theory and Methods 26, no. 6: Kulldorff, Martin. and Information Management Services, Inc. SaTScanTM v8.0: Software for the spatial and space-time scan statistics O’Loughlin, John and Frank D. W. Witmer The Localized Geographies of Violence in the North Caucasus of Russia, The Annals of the Association of American Geographers 101, no. 1 (January): 178 – 201. O’Sullivan, David and David J. Unwin Geographic Information Analysis. Hoboken, New Jersey: John Wiley and Sons. Olsen, Sjurdur F., Marco Martuzzi, and Paul Elliott Cluster analysis and disease mapping – why, when, and how? A step by step guide. British Medical Journal 313 (October): Waller, Lance A. and Carol A. Gotway Applied Spatial Statistics for Public Health Data. Hoboken, New Jersey: John Wiley and Sons.

15. Spatial Clusters and Pattern Analysis
Chris Jochem
Geog 5161 – Spring 2011