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.
Similar content being viewed by others
References
Assunção, R.M., Correa, T.R.: Surveillance to detect emerging space-time clusters. Comput. Stat. Data Anal. 53, 2817–2830 (2009)
Assunção, R.M., Costa, M., Tavares, A., Ferreira, S.: Fast detection of arbitrarily shaped disease cluster. Stat. Med. 25, 723742 (2006)
Assunção, R., Tavares, A., Kulldorff, M., Correa, T.: Space-time cluster identification in point processes. Can. J. Stat. 35, 1–17 (2007)
Baeza-Yates, R.A., Ribeiro-Neto, B.: Mod. Inform. Retr. Wiley, Boston (1999)
Corberán-Vallet, A., Lawson, A.: Conditional predictive inference for online surveillance of spatial disease incidence. Stat. Med. 30, 3095–3116 (2011)
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)
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)
Diggle, P., Rowlingson, B., Su, T.: Point process methodology for on-line spatio-temporal disease surveillance. Environmetrics 16, 423–434 (2005)
Fraker, S.E., Woodall, W.H., Mousavi, S.: Performance metrics for surveillance schemes. Quality Eng. 20, 451–464 (2008)
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)
Hardy, A.: Methods of outbreak investigation in the era of bacteriology 1880–1920. Soc. Prev. Med. 46, 355–360 (2001)
Henderson, D.: The looming threat of bioterrorism. Science 283, 1279–82 (1999)
Höhle, M.: Surveillance: an R package for the monitoring of infectious diseases. Comput. Stat. 22, 571–582 (2007)
Höhle, M., Paul, M.: Count data regression charts for the monitoring of surveillance time series. Comput. Stat. Data Anal. 52, 4357–4368 (2008)
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)
Joner, M.D., Woodall, W.H., Reynolds, M.R.: Detecting a rate increase using a Bernoulli scan statistic. Stat. Med. 27, 2555–2575 (2008)
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)
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)
Knox, E., Bartlett, M.S.: The detection of space-time interctions. J. R. Stat. Soc. C 13, 25–30 (1964)
Kulldorff, M.: A spatial scan statistic. Commun. Stat. Theory Methods 26, 1481–1496 (1997)
Kulldorff, M.: Prospective time periodic geographical disease surveillance using a scan statistic. J. R. Stat. Soc. A 164, 61–72 (2001)
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)
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)
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)
Lorden, G., Pollak, M.: Nonanticipating estimation applied to sequential analysis and changepoint detection. Ann. Stat. 33, 1422–1454 (2005)
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)
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)
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)
Patil, G., Taillie, C.: Upper level set scan statistic for detecting arbitrarily shaped hotspots. Environ. Ecol. Stat. 11, 183197 (2004)
Piroutek, A., Assunção, R., Paiva, T.: Space-time prospective surveillance based on knox local statistics. Stat. Med. 33, 2758–2773 (2014)
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)
Robertson, C., Nelson, T., MacNab, Y., Lawson, A.: Review of methods for space-time disease surveillance. Spat. Spatio Temporal Epidemiol. 1, 105–116 (2010)
Rodeiro, C., Lawson, A.: Monitoring changes in spatio-temporal maps of disease. Biom. J. 48, 463–480 (2006)
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)
Rodrigues, A., Diggle, P., Assunção, R.: Semiparametric approach to point source modellingin epidemiology and criminology. J. R. Stat. Soc. C 59, 533–542 (2010)
Rogerson, P.: Monitoring point patterns for the development of space-time clusters. J. R. Stat. Soc. A 164, 87–96 (2001)
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)
Sonesson, C., Bock, D.: A review and discussion of prospective statistical surveillance in public health. J. R. Stat. Soc. A 166, 5–21 (2003)
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)
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)
Tango, T., Takahashi, K., Kohriyamma, K.: A space-time scan statistic for detecting emerging outbreaks. Biometrics 67, 106–115 (2011)
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)
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)
Yan, P., Clayton, M.K.: A cluster model for spacetime disease counts. Stat. Med. 25(5), 867–881 (2006). doi:10.1002/sim.2424
Zhang, Z., Assunção, R., Kulldorff, M.: Spatial scan statistics adjusted for multiple clusters. J. Probab. Stat. (2010). doi:10.1155/2010/642379
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11222-016-9673-y