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MAD-STEC: a method for multiple automatic detection of space-time emerging clusters

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Abstract

Crime or disease surveillance commonly rely in space-time clustering methods to identify emerging patterns. The goal is to detect spatial-temporal clusters as soon as possible after its occurrence and to control the rate of false alarms. With this in mind, a spatio-temporal multiple cluster detection method was developed as an extension of a previous proposal based on a spatial version of the Shiryaev–Roberts statistic. Besides the capability of multiple cluster detection, the method have less input parameter than the previous proposal making its use more intuitive to practitioners. To evaluate the new methodology a simulation study is performed in several scenarios and enlighten many advantages of the proposed method. Finally, we present a case study to a crime data-set in Belo Horizonte, Brazil.

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References

  • Assunção, R.M., Correa, T.R.: Surveillance to detect emerging space-time clusters. Comput. Stat. Data Anal. 53, 2817–2830 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  • Assunção, R.M., Costa, M., Tavares, A., Ferreira, S.: Fast detection of arbitrarily shaped disease cluster. Stat. Med. 25, 723742 (2006)

    Article  MathSciNet  Google Scholar 

  • Assunção, R., Tavares, A., Kulldorff, M., Correa, T.: Space-time cluster identification in point processes. Can. J. Stat. 35, 1–17 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  • Baeza-Yates, R.A., Ribeiro-Neto, B.: Mod. Inform. Retr. Wiley, Boston (1999)

    Google Scholar 

  • Corberán-Vallet, A., Lawson, A.: Conditional predictive inference for online surveillance of spatial disease incidence. Stat. Med. 30, 3095–3116 (2011)

    Article  MathSciNet  Google Scholar 

  • Correa, T.R., Assunção, R.A., Costa, M.A.: A critical look at prospective surveillance using a scan statistic. Statistics in Medicine 34, 1081–1093 (2015)

    Article  MathSciNet  Google Scholar 

  • Demattei, C., Cucala, L.: Multiple spatio-temporal cluster detection for case event data: an ordering-based approach. Commun. Stat. Theory Methods 40, 358–372 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  • Diggle, P., Rowlingson, B., Su, T.: Point process methodology for on-line spatio-temporal disease surveillance. Environmetrics 16, 423–434 (2005)

    Article  MathSciNet  Google Scholar 

  • Fraker, S.E., Woodall, W.H., Mousavi, S.: Performance metrics for surveillance schemes. Quality Eng. 20, 451–464 (2008)

    Article  Google Scholar 

  • Gangnon, R.E.: A model for spacetime cluster detection using spatial clusters with flexible temporal risk patterns. Stat. Med. 29(22), 2325–2337 (2010). doi:10.1002/sim.3984

  • Gao, P., Guo, D., Liao, K., Webb, J.J., Cutter, S.L.: Early detection of terrorism outbreaks using prospective spacetime scan statistics. Prof. Geogr. 65(4), 676 (2013)

    Article  Google Scholar 

  • Hardy, A.: Methods of outbreak investigation in the era of bacteriology 1880–1920. Soc. Prev. Med. 46, 355–360 (2001)

    Article  Google Scholar 

  • Henderson, D.: The looming threat of bioterrorism. Science 283, 1279–82 (1999)

    Article  Google Scholar 

  • Höhle, M.: Surveillance: an R package for the monitoring of infectious diseases. Comput. Stat. 22, 571–582 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  • Höhle, M., Paul, M.: Count data regression charts for the monitoring of surveillance time series. Comput. Stat. Data Anal. 52, 4357–4368 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  • Huang, W., Cao, X., Biase, F.H., Yu, P., Zhong, S.: Time-variant clustering model for understanding cell fate decisions. Proc. Natl. Acad. Sci. 111(44), E4797–E4806 (2014)

    Article  Google Scholar 

  • Joner, M.D., Woodall, W.H., Reynolds, M.R.: Detecting a rate increase using a Bernoulli scan statistic. Stat. Med. 27, 2555–2575 (2008)

    Article  MathSciNet  Google Scholar 

  • Kenett, R.S., Pollak, M.: Data-analytic aspects of the Shiryayev-Roberts control chart: surveillance of a non-homogeneos poisson process. J. Appl. Stat. 23, 125–137 (1996)

    Article  Google Scholar 

  • Kleinman, K., Lazarus, R., Platt, R.: A generalized linear models approach for detecting incident clusters of disease in small areas, with an application to biological terrorism. Am. J. Epidemiol. 159, 217–224 (2004)

    Article  Google Scholar 

  • Knox, E., Bartlett, M.S.: The detection of space-time interctions. J. R. Stat. Soc. C 13, 25–30 (1964)

    Google Scholar 

  • Kulldorff, M.: A spatial scan statistic. Commun. Stat. Theory Methods 26, 1481–1496 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  • Kulldorff, M.: Prospective time periodic geographical disease surveillance using a scan statistic. J. R. Stat. Soc. A 164, 61–72 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  • Kulldorff, M.: Information management services, inc. satscan version 9.4.2: software for the spatial and space-time scan statistics. http://www.satscan.org (2015). Accessed 4 May 2016

  • Kulldorff, M., Heffernan, R., Hartman, J., Assunção, R., Mostashari, F.: A space-time permutation scan statistic for disease outbreak detection. PLoS Med. 2, e59 (2005)

    Article  Google Scholar 

  • Li, X.-Z., Wang, J.-F., Yang, W.-Z., Li, Z.-J., Lai, S.-J.: A spatial scan statistic for multiple clusters. Math. Biosci. 233, 135–142 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  • Lima, M.S., Duczmal, L.H.: Adaptive likelihood ratio approaches for the detection of space-time disease clusters. Comput. Stat. Data Anal. 77, 352–370 (2014)

    Article  MathSciNet  Google Scholar 

  • Lorden, G., Pollak, M.: Nonanticipating estimation applied to sequential analysis and changepoint detection. Ann. Stat. 33, 1422–1454 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  • Marshall, J., Spitzner, D., Woodall, W.: Use of the local knox statistic for the prospective monitoring of disease occurrences in space and time. Stat. Med. 7, 1579–1593 (2007)

    Article  MathSciNet  Google Scholar 

  • Neil, D., Moore, A., Sabhnani, M., Daniel, K.: Detection of emerging space-time clusters. In: KDD ’05: Proceedings of the Eleventh ACM SIGKDD International Conference on Knowledge Discovery in Data Mining, Chicago, pp. 218–227 (2005)

  • Neill, D.: Expectation-based scan statistics for monitoring spatial time series data. Int. J. Forecast. 25, 498–517 (2009)

    Article  Google Scholar 

  • Paiva, T., Assunção, R., Sim oes, T.: Prospective space-time surveillance with cumulative surfaces for geographical identification of emerging cluster. Comput. Stat. 30, 419–440 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  • Patil, G., Taillie, C.: Upper level set scan statistic for detecting arbitrarily shaped hotspots. Environ. Ecol. Stat. 11, 183197 (2004)

    MathSciNet  Google Scholar 

  • Piroutek, A., Assunção, R., Paiva, T.: Space-time prospective surveillance based on knox local statistics. Stat. Med. 33, 2758–2773 (2014)

    Article  MathSciNet  Google Scholar 

  • Prates, M., Kulldorff, M., Assunção, R.M.: Relative risk estimates from spatial and space-time scan statistics: are they biased? Stat. Med. 33, 2634–2644 (2014)

    Article  MathSciNet  Google Scholar 

  • Robertson, C., Nelson, T., MacNab, Y., Lawson, A.: Review of methods for space-time disease surveillance. Spat. Spatio Temporal Epidemiol. 1, 105–116 (2010)

    Article  Google Scholar 

  • Rodeiro, C., Lawson, A.: Monitoring changes in spatio-temporal maps of disease. Biom. J. 48, 463–480 (2006)

    Article  MathSciNet  Google Scholar 

  • Rodrigues, A., Diggle, P.J.: Bayesian estimation and prediction for inhomogeneous spatiotemporal log-gaussian cox processes using low-rank models, with application to criminal surveillance. J. Am. Stat. Assoc. 107, 93–101 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  • Rodrigues, A., Diggle, P., Assunção, R.: Semiparametric approach to point source modellingin epidemiology and criminology. J. R. Stat. Soc. C 59, 533–542 (2010)

    Article  MathSciNet  Google Scholar 

  • Rogerson, P.: Monitoring point patterns for the development of space-time clusters. J. R. Stat. Soc. A 164, 87–96 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  • Sakaki, T., Okazaki, M., Matsuo, Y.: Earthquake shakes twitter users: real-time event detection by social sensors. In: World Wide Web, pp. 851–860 (2010)

  • Sonesson, C.: A cusum framework for detection of spacetime disease clusters using scan statistics. Stat. Med. 26, 4770–4789 (2007)

    Article  MathSciNet  Google Scholar 

  • Sonesson, C., Bock, D.: A review and discussion of prospective statistical surveillance in public health. J. R. Stat. Soc. A 166, 5–21 (2003)

    Article  MathSciNet  Google Scholar 

  • Sparks, R.: Detection of spatially clustered outbreaks in motor vehicle crashes: whats the best method? Saf. Sci. 49, 794–806 (2011)

  • Streit, R.L.: Poisson Point Processes: Imaging, Tracking, and Sensing. Springer, New York (2010)

    Book  Google Scholar 

  • Takahashi, K., Kulldorff, M., Tango, T., Yih, K.: A flexibly shaped space-time scan statistic for disease outbreak detection and monitoring. Int. J. Health Geogr. 7, 14 (2008)

    Article  Google Scholar 

  • Tango, T., Takahashi, K., Kohriyamma, K.: A space-time scan statistic for detecting emerging outbreaks. Biometrics 67, 106–115 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  • Unkel, S., Farrington, C.P., Garthwaite, P.H., Robertson, C., Andrews, N.: Statistical methods for the prospective detection of infectious disease outbreaks: a review. J. R. Stat. Soc. A 175, 49–82 (2012)

    Article  MathSciNet  Google Scholar 

  • Veloso, B., Iabrudi, A., Correa, T.: Localização em tempo real de acontecimentos através de vigilância espaço-temporal de microblogs. In: IX Encontro Nacional de Inteligência Artificial. Curitiba—PR, Brazil, p. 12 (2012)

  • Woodall, W.H., Marshall, J.B., Joner, M.D., Fraker, S.E., Abdel-Salam, A.-S.G.: On the use and evaluation of prospective scan methods for health-related surveillance. J. R. Stat. Soc. A 171, 223–237 (2008)

    MathSciNet  Google Scholar 

  • Yan, P., Clayton, M.K.: A cluster model for spacetime disease counts. Stat. Med. 25(5), 867–881 (2006). doi:10.1002/sim.2424

    Article  MathSciNet  Google Scholar 

  • Zhang, Z., Assunção, R., Kulldorff, M.: Spatial scan statistics adjusted for multiple clusters. J. Probab. Stat. (2010). doi:10.1155/2010/642379

Download references

Acknowledgments

The authors would like to thank the kind suggestions and insights provided by Renato Martins Assunção that helped to improve the manuscript. Also, the third author would like to thank FAPEMIG-Brazil and CNPq-Brazil for partial financial support. The authors would also like to thank the referees for the interesting comments that improved the paper.

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Correspondence to Thais R. Correa.

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Veloso, B.M., Correa, T.R., Prates, M.O. et al. MAD-STEC: a method for multiple automatic detection of space-time emerging clusters. Stat Comput 27, 1099–1110 (2017). https://doi.org/10.1007/s11222-016-9673-y

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  • DOI: https://doi.org/10.1007/s11222-016-9673-y

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