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Clusters in Aggregated Health Data

  • Kevin Buchin
  • Maike Buchin
  • Marc van Kreveld
  • Maarten Löffler
  • Jun Luo
  • Rodrigo I. Silveira
Conference paper
Part of the Lecture Notes in Geoinformation and Cartography book series (LNGC)

Abstract

Spatial information plays an important role in the identification of sources of outbreaks for many different health-related conditions. In the public health domain, as in many other domains, the available data is often aggregated into geographical regions, such as zip codes or municipalities.

In this paper we study the problem of finding clusters in spatially aggregated data. Given a subdivision of the plane into regions with two values per region, a case count and a population count, we look for a cluster with maximum density. We model the problem as finding a placement of a given shape R such that the ratio of cases contained in R to people living in R is maximized. We propose two models that differ on how to determine the cases in R, together with several variants and extensions, and give algorithms that solve the problems efficiently.

Keywords

cluster outbreak algorithm aggregated data. 

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References

  1. 1.
    R. Agrawal, J. Gehrke, D. Gunopulus, and P. Raghavan. Automatic subspace clustering of high dimensional data for data mining applications. In Proc. ACM-SIGMOD Intl. Conf. on Mgmt. of Data, pages 94–105, 1998.Google Scholar
  2. 2.
    H. Brody, M. R. Rip, P. Vinten-Johansen, N. Paneth, and S. Rachman. Map-making and myth-making in Broad Street: the London cholera epidemic, 1854. The Lancet, 356:64–68, 2000.CrossRefGoogle Scholar
  3. 3.
    N. Cleave, P. Brown, and C. Payne. Methods for ecological inference: an evaluation. Journal of the Royal Statistical Society, Series A, 158:55–75, 1995.Google Scholar
  4. 4.
    L. H. Cox. Protecting confidentiality in small population health and environmental statistics. Stat. Med., 15:1895–1905, 1996.CrossRefGoogle Scholar
  5. 5.
    E. Cromley and S. McLafferty. GIS and Public Health. The Guilford Press, New York, 2002.Google Scholar
  6. 6.
    J. W. Den Boer, L. Verhoef, M. A. Bencini, J. P. Bruin, R. Jansen, and E. P. Yzerman. Outbreak detection and secondary prevention of legionnaires disease: A national approach. International Journal of Hygiene and Environmental Health, 210:1–7, 2007.CrossRefGoogle Scholar
  7. 7.
    M. Ester, H. Kriegel, J. Sander, and X. Xu. A density-based algorithm for discovering clusters in large spatial databases with noise. In Proc. 2nd International Conference on Knowledge Discovery and Data Mining, pages 226–231, 1996.Google Scholar
  8. 8.
    A. Gilsdorf, C. Kroh, S. Grimm, E. Jensen, C. Wagner-Wiening, and K. Alpers. Large Q fever outbreak due to sheep farming near residential areas. Accepted for publication to Epidemiol. Infect., 2007.Google Scholar
  9. 9.
    J. Han and M. Kamber. Data Mining: Concepts and Techniques. Academic Press, San Diego, 2001.Google Scholar
  10. 10.
    J. Hartigan. Clustering Algorithms. John Wiley & Sons, New York, 1975.Google Scholar
  11. 11.
    A. Jain and R. Dubes. Algorithms for Clustering Data. Prentice Hall, Englewood Cliffs, New Jersey, 1988.Google Scholar
  12. 12.
    G. King. A Solution to the Ecological Inference Problem. Princeton University Press, Princeton, New Jersey, 1997.Google Scholar
  13. 13.
    M. Kulldorff. A spatial scan statistic. Communications in Statistics: Theory and Methods, 26,:1481–1496, 1997.CrossRefGoogle Scholar
  14. 14.
    M. Kulldorff and N. Nagarwalla. Spatial disease clusters: detection and inference. Stat. Med., 14:799–810, 1995.Google Scholar
  15. 15.
    S. Openshaw. The Modifiable Areal Problem. CATMOG No.38. Geo Books, Norwich, 1984.Google Scholar
  16. 16.
    S. Openshaw, M. Charlton, C. Wymer, and A. Craft. A Mark 1 Geographical Analysis Machine for the automated analysis of point data sets. Int. J. Geographical Information Systems, 1:335–358, 1987.CrossRefGoogle Scholar
  17. 17.
    P. Phillips and I. Lee. Areal aggregated crime reasoning through density tracing. In Proc. International Workshop on Spatial and Spatio-temporal Data Mining, 2007.Google Scholar
  18. 18.
    I. Reinbacher, M. van Kreveld, and M. Benkert. Scale dependent definitions of gradient and aspect and their computation. In A. Riedl, W. Kainz, and G. A. Elmes, editors, Proc. 12th Intern. Symp. Spatial Data Handling (SDH’06), pages 863–879, 2006.Google Scholar
  19. 19.
    W. Robinson. Ecological correlations and the behavior of individuals. American Sociological Reviews, 15:351–357, 1950.CrossRefGoogle Scholar
  20. 20.
    M. Sharir. On k-sets in arrangements of curves and surfaces. Discrete Comput. Geom., 6:593–613, 1991.CrossRefGoogle Scholar
  21. 21.
    J. Snow. On the Mode of Communication of Cholera. Churchill Livingstone, London, 2nd edition, 1854.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Kevin Buchin
    • 1
  • Maike Buchin
    • 1
  • Marc van Kreveld
    • 1
  • Maarten Löffler
    • 1
  • Jun Luo
    • 1
  • Rodrigo I. Silveira
    • 1
  1. 1.Department of Information and Computing SciencesUtrecht Universitythe Netherlands

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