Outbreak Detection Of Spatio-Temporally Smoothed Crashes

Ross Sparks, Chris Okugami, Sarah Bolt

CSIRO Mathematics, Informatics and Statistics, Sydney, Australia.
CSIRO Sustainable Ecosystems, Carmody Road, St. Lucia Queensland, Australia.

DOI: 10.4236/ojsst.2012.23013                

Abstract

Spatio-temporal surveillance methods for detecting outbreaks are common with the SCAN statistic setting the benchmark. If the shape and size of the outbreaks are known, then the SCAN statistic can be trained to efficiently detect these, however this is seldom the case. Therefore devising a plan that is efficient at detecting a range of outbreaks that vary in size and shape is important in practical applications. So this paper introduces a method called EWMA Surveillance Trees that uses a binary recursive partitioning approach to locate and detect outbreaks. This approach is explained and then its performance is compared to that of the SCAN statistic in a series of simulation studies. While the SCAN statistic is shown to remain the most effective at detecting outbreaks of a known shape and size, the EWMA Surveillance Trees are shown to be more robust. The method is also applied to an example of actual data from motor vehicle crashes in an area of Sydney Australia from 2000 to 2004 in order to detect dates and geographic regions with outbreaks of crashes above the expected.

Keywords

Average Run Length; Exponential Weighted Moving Averages; Monitoring; Spatial Outbreaks; Spatio-Temporal Smoothing; Crash Outbreaks

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	M. Kulldorff, “Prospective Time Periodic Geographical Disease Surveillance Using a SCAN Statistic,” Journal of the Royal Statistical Society Series A—Statistics in Society, Vol. 164, No. 1, 2001, pp. 61-72. doi:10.1111/1467-985X.00186
[2]	M. Kulldorff and N. Nagarwalla, “Spatial Disease Clusters: Detection and Inference,” Statistics in Medicine, Vol. 14, No. 8, 1995, pp. 799-810. doi:10.1002/sim.4780140809
[3]	M. Kulldorff, “A Spatial SCAN Statistic,” Communications in Statistics: Theory and Methods, Vol. 26, 1997, pp. 1481-1496. doi:10.1080/03610929708831995
[4]	M. Kulldorff, R. Heffernan, J. Hartman, R. M. Assun??o and F. Mostashari, “A Space-Time Permutation SCAN Statistic for the Early Detection of Disease Outbreaks,” PLoS Medicine, Vol. 2, No. 3, 2005, pp. 216-224. doi:10.1371/journal.pmed.0020059
[5]	W. H. Woodall, J. B. Marshall, M. D. Joner Jr., J. E. Fraker and A. G. Abdel-Salam, “On the Use and Evaluation of Prospective SCAN Methods for Health-Related Surveillance,” Journal of the Royal Statistical Society: Series A, Vol. 171, No. 1, 2008, pp. 223-237.
[6]	S. W. Han, Y. Mei and K.-L. Tsui, “A Comparison between SCAN and CUSUM Methods for Detecting Increases in Poisson Rates,” Technical Report, School of ISyE, Georgia Institute of Technology, 2008.
[7]	R. F. Raubertas, “An Analysis of Disease Surveillance Data That Uses the Geographic Locations of Reporting Units,” Statistics in Medicine, Vol. 18, 1989, pp. 2111-2122.
[8]	P. A. Rogerson and I. Yamada, “Monitoring Change in Spatial Patterns of Disease: Comparing Univariate and Multivariate Cumulative Sum Approaches,” Statistics in Medicine, Vol. 23, No. 14, 2004, pp. 2195-2214. doi:10.1002/sim.1806
[9]	J. Glaz, J. Naus and S. Wallenstein, “SCAN Statistics,” Springer, New York, 2001.
[10]	J. Chen and J. Glaz, “Two-Dimensional Discrete Scan Statistics,” Statistics and Probability Letters, Vol. 31, No. 1, 1996, pp. 59-68. doi:10.1016/0167-7152(95)00014-3
[11]	R. Sparks, C. Carter, P. L. Graham, D. Muscatello, T. Churches, J. Kaldor, R. Turner, W. Zheng and L. Ryan, “Understanding Sources of Variation in Syndromic Surveillance for Early Warning of Natural or Intentional Disease Outbreaks,” IIE Transactions, Vol. 42, No. 9, 2010, pp. 613-631. doi:10.1080/07408170902942667
[12]	R. S. Sparks and C. Okugami, “Surveillance Trees: Early Detection of Unusually High Number of Vehicle Crashes,” 2009. http://interstat.statjournals.net/YEAR/2010/abstracts/1001002.php