Abstract
In epidemiological studies, it is often of interest to evaluate whether a disease is randomly distributed over time and/or space after being adjusted for a known heterogeneity, which may provide clues to the etiology of disease. To do this, we can apply tests for spatial randomness, or disease clustering. In this paper, I review the existing tests for disease clustering and discuss the advantages and disadvantages of these test statistics. These tests are illustrated and compared with several real temporal and spatial data sets.
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References
Assunção R., Costa M., Tavares A. and Ferreira S. (2006). Fast detection of arbitrarily shaped disease clusters, Statistics in Medicine, 25, 723–742.
Bailar III J.C., Eisenberg H. and Mantel N. (1970). Time between pairs of leukemia cases, Cancer, 25, 1301–1303.
Besag J.E. and Newell J. (1991). The detection of clusters in rare diseases, Journal of the Royal Statistical Society, Series A, 154, 143–155.
Bonetti M. and Pagano M. (2005). The interpoint distance distribution as a descriptor of point patterns, with an application to spatial disease clustering, Statistics in Medicine, 24, 753–773.
Cuzick J.C. and Edwards R. (1990). Spatial clustering for inhomogeneous populations, Journal of the Royal Statistical Society, Series B, 52, 73–104.
Duczmal L. and Assunção R. (2004). A simulated annealing strategy for the detection of arbitrarily shaped clusters, Computational Statistics and Data Analysis, 45, 269–286.
Dwass M. (1957). Modified randomization test for nonparametric hypotheses, Annals of Mathematical Statistics, 28, 181–187.
Ederer F., Myers M.H. and Mantel N. (1964). A statistical problem in space and time: do leukemia cases come in clusters? Biometrika, 20, 626–638.
Geary R.C. (1954). The contiguity ratio and statistical mapping, The Incorporated Statistician, 5, 115–145.
Grimson R.C., Wang K.C. and Johnson P.W.C. (1981). Searching for hierarchical clusters of disease: spatial patterns of sudden infant death syndrome, Social Science & Medicine, 15D, 287–293. Hechtor H.H. and Borhan N.O. (1965).
Knox G. (1959). Secular pattern of congenital oesophageal atresia, British Journal of Preventive Social Medicine, 13, 222–226.
Knox E.G. and Lancashire R. (1982). Detection of minimal epidemics, Statistics in Medicine, 1, 183–189.
Kulldorff M. (1997). A spatial scan statistic, Communications in Statistics: Theory and Methods, 26, 1481–1496.
Kulldorff M. (1998). Statistical methods for spatial epidemiology: tests for randomness. In GIS and Health, (Ed., Gatrell A. and Loytonen M.), 49–62, Taylor & Francis, London.
Kulldorff M. (2006). Tests for spatial randomness adjusted for an inhomogeneity: a general framework, Journal of American Statistical Association, 101, 1289–1305.
Kulldorff M. and Nagarwalla N. (1995). Spatial disease clusters: detection and inference, Statistics in Medicine, 14, 799–810.
Kulldorff M., Tango T. and Park P.J. (2003). Power comparisons for disease clustering tests, Computational Statistics and Data Analysis, 42, 665–684.
Kulldorff M. and Information Management Services, Inc. (2007). SaTScan v7.0: Software for the spatial and space-time scan statistics, http://www.satscan.org/
Larsen R.J., Holmes C.L. and Heath C.W. (1973). A statistical test for measuring unimodal clustering: a description of the test and of its application to cases of acute leukemia in metropolitan Atlanta, Georgia, Biometrics, 29, 301–309.
Lawson A.B., Browne W.J. and Vidal Rodeiro C.L. (2003). Disease Mapping with WinBUGS and MLwiN, John Wiley & Sons, Chichester.
Lawson A.B. and Kleinman K. (eds.) (2005). Spatial & Syndromic Surveillance for Public Health, John Wiley & Sons, New York
Mantel N., Kryscio R.J. and Myers M.H. (1976). Tables and formulas for extended use of the Ederer-Myers-Mantel disease clustering procedure, American Journal of Epidemiology, 104, 576–584.
Molinari N., Bonaldi, C. and Daures, J.P. (2001). Multiple temporal cluster detection. Biometrics, 57, 577–583.
Nagarwalla N. (1996). A scan statistic with a variable window. Statistics in Medicine, 15, 845–850.
Naus J.I. (1965). The distribution of the size of the maximum cluster of points on a line, Journal of the American Statistical Association, 60, 532–538.
Naus J.I. (1966). A power comparison of two tests of non-random clustering, Technometrics, 8, 493–517.
Ohno Y., Aoki K. and Aoki N. (1979). A test of significance for geographic clusters of disease, International Journal of Epidemiology, 8, 273–281.
Ohno Y. and Aoki K. (1981). Cancer deaths by city and county in Japan: a test of significance for geographic clustering of disease, Social Science & Medicine, 15D, 251–258.
Openshaw S., Craft A.W., Charlton M. and Birth J.M. (1988). Investigation of leukemia clusters by use of a geographical analysis machine, Lancet, 1(8580), 272–273.
Patil G. P. and Taillie C. (2004). Upper level set scan statistic for detecting arbitrarily shaped hotspots, Environmental and Ecological Statistics, 11, 183–197.
Song C. and Kulldorff M. (2003). Power evaluation of disease clustering tests, International Journal of Health Geographics, 2, 9.
Song C. and Kulldorff M. (2005). Tango’s maximized excess events test with different weights, International Journal of Health Geographics, 4, 32.
Takahashi K., Yokoyama T. and Tango T. (2007). FleXScan: Software for the Flexble Scan Statistic. v2.0. http://www.niph.go.jp/soshiki/gijutsu/ index_e.html/.
Tango T. (1984). The detection of disease clustering in time, Biometrics, 40, 15–26.
Tango T. (1990). Asymptotic distribution of an index for disease clustering, Biometrics, 46, 351–357.
Tango T. (1995). A class of tests for detecting “general” and “focused” clustering of rare diseases, Statistics in Medicine, 14, 2323–2334.
Tango T. (1999). Comparison of general tests for disease clustering, In Disease Mapping and Risk Assessment for Public Health, (Ed., A.B. Lawson et al.), pp. 111–117, Wiley & Sons, New York.
Tango T. (2000). A test for spatial disease clustering adjusted for multiple testing, Statistics in Medicine, 19, 191–204.
Tango T. and Takahashi K. (2005). A flexibly shaped spatial scan statistic for detecting clusters, International Journal of Health Geographics, 4, 11. http://www.ij-healthgeographics.com/content/4/1/11
Tango T. (2007). A class of multiplicity adjusted tests for spatial clustering based on case-control point data, Biometrics, 63, 119–127.
Turnbull B.W., Iwano E.J., Burnnett W.S., Howe H.L. and Clark LC. (1990). Monitoring for clusters of disease: application to leukemia incidence in upstate New York, American Journal of Epidemiology, 132, suppl. S136–143.
Wallenstein S. (1980). A test for detection of clustering over time, American Journal of Epidemiology, 111, 367–372.
Wallenstein S. and Neff N. (1987). An approximation for the distribution of the scan statistic. Statistics in Medicine, 6, 197–207.
Weinstock M.A. (1981). A generalized scan statistic test for the detection of clusters, International Journal of Epidemiology, 10, 289–93.
Whittemore A. and Keller J.B. (1986). A letter to the editor. On Tango’s index of disease clustering in time, Biometrics, 42, 218.
Whittemore A.S., Friend N., Brown B.W. and Holly E.A. (1987). A test to detect clusters of disease, Biometrika, 74, 631–635.
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Tango, T. (2009). Detection of Disease Clustering. In: Glaz, J., Pozdnyakov, V., Wallenstein, S. (eds) Scan Statistics. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4749-0_17
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DOI: https://doi.org/10.1007/978-0-8176-4749-0_17
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