Skip to main content
SpringerLink
Log in

Health Monitoring Techniques Using Scan Statistics

  • Living reference work entry
  • First Online:
Handbook of Scan Statistics

  • 264 Accesses

Abstract

Scan statistics appeared in the statistics literature about half a century ago, and since then many papers suggesting either extensions and modifications or applications into various research fields have been published. Scan statistics are mainly used to detect clusters of events in time or space. In the last two decades several researchers have proposed techniques or systems for the surveillance of public health or other healthcare processes. In this paper, we shall present a systematic review of health monitoring techniques which exploit scan statistics in order to set up early warning systems detecting potential threats for public health.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

References

  • Balakrishnan N, Koutras MV (2011) Runs and scans with applications. Wiley, New York

    MATH  Google Scholar 

  • Bersimis S, Chalkias C, Anthopoulou T (2014) Detecting and interpreting clusters of economic activity in rural areas using scan statistic and Lisa under a unified framework. Appl Stoch Models Bus Ind 30 (5): 573–587

    Article  MathSciNet  Google Scholar 

  • Bersimis S, Sachlas A, Castagliola P (2017a) Controlling bivariate categorical processes using scan rules. Methodol Comput Appl Probab 19 (4): 1135–1149

    Article  MathSciNet  MATH  Google Scholar 

  • Bersimis S, Sachlas A, Papaioannou T (2018a) Monitoring phase II comparative clinical trials with two endpoints and penalty for adverse events. Methodol Comput Appl Probab 20 (2): 719–738

    Article  MathSciNet  MATH  Google Scholar 

  • Bersimis S, Sachlas A, Sparks R (2017b) Performance monitoring and competence assessment in health services. Methodol Comput Appl Probab 19 (4): 1169–1190

    Article  MathSciNet  MATH  Google Scholar 

  • Bersimis S, Sgora A, Psarakis S (2018b) The application of multivariate statistical process monitoring in non-industrial processes. Qual Technol Quantit Manag 15 (4): 526–549

    Article  Google Scholar 

  • Bhatt V, Tiwari N (2014) A spatial scan statistic for survival data based on weibull distribution. Stat Med 33 (11):1867–1876

    Article  MathSciNet  Google Scholar 

  • Boscoe FP, McLaughlin C, Schymura MJ, Kielb CL (2003) Visualization of the spatial scan statistic using nested circles. Health Place 9 (3): 273–277

    Article  Google Scholar 

  • Burkom HS (2003) Biosurveillance applying scan statistics with multiple, disparate data sources. J. Urban Health 80 (1): i57–i65

    Article  Google Scholar 

  • Cançado AL, da Silva CQ, da Silva MF (2014) A spatial scan statistic for zero-inflated poisson process. Environ Ecol Stat 21 (4): 627–650

    Article  MathSciNet  Google Scholar 

  • Cançado AL, Fernandes LB, da Silva CQ (2017) A Bayesian spatial scan statistic for zero-inflated count data. Spat Stat 20: 57–75

    Article  MathSciNet  Google Scholar 

  • Charras-Garrido M, Azizi L, Forbes F, Doyle S, Peyrard N, Abrial D (2013) On the difficulty to delimit disease risk hot spots. Int J Appl Earth Obs Geoinf 22: 99–105

    Article  Google Scholar 

  • Chen D, Cunningham J, Moore K, Tian J (2011) Spatial and temporal aberration detection methods for disease outbreaks in syndromic surveillance systems. Ann GIS 17 (4): 211–220

    Article  Google Scholar 

  • Chen H, Zeng D, Yan P (2010) Infectious disease informatics: syndromic surveillance for public health and bio-defense. Springer, Boston

    Book  Google Scholar 

  • Chen J, Glaz J (1996) Two-dimensional discrete scan statistics. Stat Probab Lett 31 (1): 59–68

    Article  MathSciNet  MATH  Google Scholar 

  • Chen J, Glaz J (1997) Approximations and inequalities for the distribution of a scan statistic for 0-1 bernoulli trials. Adv Theory Pract Stat 1: 285–298

    MathSciNet  MATH  Google Scholar 

  • Cheung YTD, Spittal MJ, Williamson MK, Tung SJ, Pirkis J (2013) Application of scan statistics to detect suicide clusters in australia. PLOS ONE (1): 1–11

    Google Scholar 

  • Costa MA, Kulldorff M (2009) Applications of spatial scan statistics: a review. Birkhäuser, Boston, pp 129–152

    Google Scholar 

  • Cucala L (2008) A hypothesis-free multiple scan statistic with variable window. Biom J 50 (2): 299–310

    Article  MathSciNet  Google Scholar 

  • Cucala L (2009) A flexible spatial scan test for case event data. Comput Stat Data Analy 53 (8): 2843–2850

    Article  MathSciNet  MATH  Google Scholar 

  • Cucala L, Genin M, Lanier C, Occelli F (2017) A multivariate gaussian scan statistic for spatial data. Spat Stat 21: 66–74

    Article  MathSciNet  Google Scholar 

  • Darling R, Waterman M (1986) Extreme value distribution for the largest cube in a random lattice. SIAM J Appl Math 46 (1): 118–132

    Article  MathSciNet  MATH  Google Scholar 

  • Duczmal L, Assuncao R (2004) A simulated annealing strategy for the detection of arbitrarily shaped spatial clusters. Comput Stat Data Anal 45 (2): 269–286

    Article  MathSciNet  MATH  Google Scholar 

  • Duczmal L, Buckeridge DL (2006) A workflow spatial scan statistic Stat Med 25 (5): 743–754

    Article  MathSciNet  Google Scholar 

  • Duczmal L, Kulldorff M, Huang L (2006) Evaluation of spatial scan statistics for irregularly shaped clusters. J Comput Graph Stat 15 (2): 428–442

    Article  MathSciNet  Google Scholar 

  • Ebneshahrashoob M, Gao T, Wu M (2005) An efficient algorithm for exact distribution of discrete scan statistics. Methodol Comput Appl Probab 7 (4): 459–471

    Article  MathSciNet  MATH  Google Scholar 

  • Faires MC, Pearl DL, Ciccotelli WA, Berke O, Reid-Smith RJ, Weese JS (2014) The use of the temporal scan statistic to detect methicillin-resistant staphylococcus aureus clusters in a community hospital. BMC Infect Dis 14 (1): 375

    Article  Google Scholar 

  • Fraker SE (2007) Evaluation of scan methods used in the monitoring of public health surveillance data. PhD thesis, Virginia Tech

    Google Scholar 

  • Fu J, Koutras M (1994) Poisson approximations for 2-dimensional patterns. Ann Inst Stat Math 46 (1): 179–192

    Article  MathSciNet  MATH  Google Scholar 

  • Gallego B, Sintchenko V, Wang Q, Hiley L, Gilbert GL, Coiera E (2009) Biosurveillance of emerging biothreats using scalable genotype clustering. J Biomed Inform 42 (1): 66–73

    Article  Google Scholar 

  • Glaz J, Naus J, Wallenstein S (2001) Scan statistics. Graduate texts in mathematics. Springer, New York/London

    Book  MATH  Google Scholar 

  • Hall DB (2000) Zero-inflated poisson and binomial regression with random effects: a case study. Biometrics 56 (4): 1030–1039

    Article  MathSciNet  MATH  Google Scholar 

  • Han SW, Tsui K-L, Ariyajunya B, Kim SB (2010) A comparison of CUSUM, EWMA, and temporal scan statistics for detection of increases in poisson rates. Qual Reliab Eng Int 26 (3): 279–289

    Article  Google Scholar 

  • Hanslik T, Boelle P-Y, Flahault A (2001) The control chart: an epidemiological tool for public health monitoring. Public Health 115 (4): 277–281

    Google Scholar 

  • Heffernan R, Mostashari F, Das D, Karpati A, Kulldorff M, Weiss D et al (2004) Syndromic surveillance in public health practice, New York city. Emerg Infect Dis 10 (5): 858–864

    Article  Google Scholar 

  • Hjalmars U, Kulldorff M, Gustafsson G, Nagarwalla N (1996) Childhood leukaemia in Sweden: using GIS and a spatial scan statistic for cluster detection. Stat Med 15 (7–9): 707–715

    Article  Google Scholar 

  • Hsu CE, Jacobson H, Mas FS (2004) Evaluating the disparity of female breast cancer mortality among racial groups-a spatiotemporal analysis. Int J Health Geogr 3 (1): 4

    Article  Google Scholar 

  • Huang L, Kulldorff M, Gregorio D (2007) A spatial scan statistic for survival data. Biometrics 63 (1): 109–118

    Article  MathSciNet  MATH  Google Scholar 

  • Huang L, Tiwari RC, Zou Z, Kulldorff M, Feuer EJ (2009) Weighted normal spatial scan statistic for heterogeneous population data. J Am Stat Assoc 104 (487): 886–898

    Article  MathSciNet  MATH  Google Scholar 

  • Huang SS, Yokoe DS, Stelling J, Placzek H, Kulldorff M, Kleinman K, O’Brien TF, Calderwood MS, Vostok J, Dunn J et al (2010) Automated detection of infectious disease outbreaks in hospitals: a retrospective cohort study. PLoS Med 7 (2): e1000238

    Article  Google Scholar 

  • Imanishi M, Newton AE, Vieira AR, Gonzales-Aviles G, Kendall Scott ME, Manikonda K, Maxwell TN, Halpin JL, Freeman MM, Medalla F et al (2015) Typhoid fever acquired in the united states, 1999–2010: epidemiology, microbiology, and use of a space-time scan statistic for outbreak detection. Epidemiol Infect 143 (11): 2343–2354

    Article  Google Scholar 

  • Ismail NA, Pettitt AN, Webster RA (2003) “online” monitoring and retrospective analysis of hospital outcomes based on a scan statistic. Stat Med 22 (18): 2861–2876

    Article  Google Scholar 

  • Jiang X, Neill DB, Cooper GF (2010) A Bayesian network model for spatial event surveillance. Int J Approx Reason 51 (2): 224–239

    Article  Google Scholar 

  • Joner MD Jr, Woodall WH, Reynolds MR Jr (2008) Detecting a rate increase using a bernoulli scan statistic. Stat Med 27 (14): 2555–2575

    Article  MathSciNet  Google Scholar 

  • Jung I, Cho HJ (2015) A nonparametric spatial scan statistic for continuous data. Int J Health Geogr 14 (1): 30

    Article  Google Scholar 

  • Jung I, Kulldorff M, Klassen AC (2007) A spatial scan statistic for ordinal data. Stat Med 26 (7): 1594–1607

    Article  MathSciNet  Google Scholar 

  • Jung I, Kulldorff M, Richard OJ (2010) A spatial scan statistic for multinomial data. Stat Med 29 (18): 1910–1918

    Article  MathSciNet  Google Scholar 

  • Kedem B, Wen S (2007) Semi-parametric cluster detection. J Stat Theory Pract 1 (1): 49–72

    Article  MathSciNet  MATH  Google Scholar 

  • Klassen AC, Kulldorff M, Curriero F (2005) Geographical clustering of prostate cancer grade and stage at diagnosis, before and after adjustment for risk factors. Int J Health Geogr 4 (1): 1

    Article  Google Scholar 

  • Kleinman K, Abrams A, Kulldorff M, Platt R (2005) A model-adjusted space-time scan statistic with an application to syndromic surveillance. Epidemiol Infect 133 (3): 409–419

    Article  Google Scholar 

  • Koutras M, Alexandrou V (1995) Runs, scans and urn model distributions: a unified Markov chain approach. Ann Inst Stat Math 47 (4): 743–766

    Article  MathSciNet  MATH  Google Scholar 

  • Kulldorff M (1997) A spatial scan statistic. Commun Stat Theory Methods 26 (6): 1481–1496

    Article  MathSciNet  MATH  Google Scholar 

  • Kulldorff M (2001) Prospective time periodic geographical disease surveillance using a scan statistic. J R Stat Soc Ser A (Stat Soc) 164 (1): 61–72

    Article  MathSciNet  MATH  Google Scholar 

  • Kulldorff M, Athas WF, Feurer EJ, Miller BA, Key CR (1998) Evaluating cluster alarms: a space-time scan statistic and brain cancer in Los Alamos, New Mexico. Am J Public Health 88 (9): 1377–1380

    Article  Google Scholar 

  • Kulldorff M, Fang Z, Walsh SJ (2003) A tree-based scan statistic for database disease surveillance. Biometrics 59 (2): 323–331

    Article  MathSciNet  MATH  Google Scholar 

  • Kulldorff M, Feuer EJ, Miller BA, Freedma LS (1997) Breast cancer clusters in the northeast united states: A geographic analysis. Am J Epidemiol 146 (2): 161–170

    Article  Google Scholar 

  • Kulldorff M, Heffernan R, Hartman J, Assunção R, Mostashari F (2005) A space-time permutation scan statistic for disease outbreak detection. PLoS Med 2 (3): e59

    Article  Google Scholar 

  • Kulldorff M, Huang L, Konty K (2009) A scan statistic for continuous data based on the normal probability model. Int J Health Geogr 8 (1): 58

    Article  Google Scholar 

  • Kulldorff M, Huang L, Pickle L, Duczmal L (2006) An elliptic spatial scan statistic. Stat Med 25 (22): 3929–3943

    Article  MathSciNet  Google Scholar 

  • Kulldorff M, Mostashari F, Duczmal L, Yih W, Kleinman K, Platt R (2007) Multivariate scan statistics for disease surveillance. Stat Med 26 (8): 1824–1833

    Article  MathSciNet  Google Scholar 

  • Kulldorff M, Nagarwalla N (1995) Spatial disease clusters: detection and inference. Stat Med 14 (8): 799–810

    Article  Google Scholar 

  • Leibovici DG, Bastin L, Anand S, Hobona G, Jackson M (2011) Spatially clustered associations in health related geospatial data. Trans GIS 15 (3): 347–364

    Article  Google Scholar 

  • Lombardo J, Burkom H, Elbert E, Magruder S, Lewis SH, Loschen W, Sari J, Sniegoski C, Wojcik R, Pavlin J (2003) A systems overview of the electronic surveillance system for the early notification of community-based epidemics (essence II). J Urban Health 80 (1): i32–i42

    Google Scholar 

  • Nagarwalla N (1996) A scan statistic with a variable window. Stat Med 15 (7-9): 845–850

    Article  Google Scholar 

  • Naus JI (1965a) Clustering of random points in two dimensions. Biometrika 52 (1/2): 263–267

    Article  MathSciNet  MATH  Google Scholar 

  • Naus JI (1965b) The distribution of the size of the maximum cluster of points on a line. J Am Stat Assoc 60 (310): 532–538

    Article  MathSciNet  Google Scholar 

  • Naus J, Wallenstein S (2006) Temporal surveillance using scan statistics. Stat Med 25 (2): 311–324

    Article  MathSciNet  Google Scholar 

  • Neill DB (2009) An empirical comparison of spatial scan statistics for outbreak detection. Int J Health Geogr 8 (1): 20

    Article  Google Scholar 

  • Neill DB (2011) Fast Bayesian scan statistics for multivariate event detection and visualization. Stat Med 30 (5): 455–469

    Article  MathSciNet  Google Scholar 

  • Neill DB, Cooper GF (2010) A multivariate Bayesian scan statistic for early event detection and characterization. Mach Learn 79 (3): 261–282

    Article  MathSciNet  Google Scholar 

  • Neill DB, McFowland E, Zheng H (2013) Fast subset scan for multivariate event detection. Stat Med 32 (13): 2185–2208

    Article  MathSciNet  Google Scholar 

  • Neill DB, Moore AW, Cooper GF (2006) A Bayesian spatial scan statistic. In: Advances in neural information processing systems, pp 1003–1010

    Google Scholar 

  • Odoi A, Martin SW, Michel P, Middleton D, Holt J, Wilson J et al (2004) Investigation of clusters of giardiasis using GIS and a spatial scan statistic. Int J Health Geogr 3 (1): 11

    Article  Google Scholar 

  • Ozdenerol E, Williams BL, Kang SY, Magsumbol MS (2005) Comparison of spatial scan statistic and spatial filtering in estimating low birth weight clusters. Int J Health Geogr 4 (1): 19

    Article  Google Scholar 

  • Sabel CE, Boyle P, Löytönen M, Gatrell AC, Jokelainen M, Flowerdew R, Maasilta P (2003) Spatial clustering of amyotrophic lateral sclerosis in finland at place of birth and place of death. Am J Epidemiol 157 (10): 898–905

    Article  Google Scholar 

  • Sabhnani MR, Neill DB, Moore AW (2005) Detecting anomalous patterns in pharmacy retail data. In: Data mining methods anomaly detection, vol 58

    Google Scholar 

  • Sheehan TJ, DeChello LM (2005) A space-time analysis of the proportion of late stage breast cancer in Massachusetts, 1988 to 1997. Int J Health Geogr 4 (1): 15

    Article  Google Scholar 

  • Sheng K, Naus J (1996) Matching fixed rectangles in 2-dimension. Stat Probab Lett 26 (1): 83–90

    Article  MathSciNet  MATH  Google Scholar 

  • So HC, Pearl DL, von Königslöw T, Louie M, Chui L, Svenson LW (2013) Spatiotemporal scan statistics for the detection of outbreaks involving common molecular subtypes: using human cases of escherichia coli o157:h7 provincial pfge pattern 8 (national designation ecxai.0001) in Alberta as an example. Zoonoses Public Health 60 (5): 341–348

    Article  Google Scholar 

  • Sonesson C (2007) A CUSUM framework for detection of space-time disease clusters using scan statistics. Stat Med 26 (26): 4770–4789

    Article  MathSciNet  Google Scholar 

  • Staubach C, Schmid V, Knorr-Held L, Ziller M (2002) A bayesian model for spatial wildlife disease prevalence data. Prev Vet Med 56 (1): 75–87

    Article  Google Scholar 

  • Takahashi K, Kulldorff M, Tango T, Yih K (2008) A flexibly shaped space-time scan statistic for disease outbreak detection and monitoring. Int J Health Geogr 7 (1): 14

    Article  Google Scholar 

  • Takahashi K, Yokoyama T, Tango T (2010) FleXScan user guide

    Google Scholar 

  • Tango T (2008) A spatial scan statistic with a restricted likelihood ratio. Jpn J Biom 29 (2): 75–95

    Article  Google Scholar 

  • Tango T, Takahashi K (2005) A flexibly shaped spatial scan statistic for detecting clusters. Int J Health Geogr 4 (1): 11

    Article  Google Scholar 

  • Tango T, Takahashi K (2012) A flexible spatial scan statistic with a restricted likelihood ratio for detecting disease clusters. Stat Med 31 (30): 4207–4218

    Article  MathSciNet  Google Scholar 

  • Tango T, Takahashi K, Kohriyama K (2011) A space-time scan statistic for detecting emerging outbreaks. Biometrics 67 (1): 106–115

    Article  MathSciNet  MATH  Google Scholar 

  • Taylor SR, Arrowsmith SJ, Anderson DN (2010) Detection of short time transients from spectrograms using scan statistics. Bull Seismol Soc Am 100 (5A): 1940–1951

    Article  Google Scholar 

  • Tsui K-L, Chiu W, Gierlich P, Goldsman D, Liu X, Maschek T (2008) A review of healthcare, public health, and syndromic surveillance. Qual Eng 20 (4): 435–450

    Article  Google Scholar 

  • Wagner M, Moore A, Aryel R (2011) Handbook of biosurveillance. Elsevier Science, Burlington

    Google Scholar 

  • Wallested S, Gould MS, Kleinmaw M (1989) Use of the scan statistic to detect time-space clustering. Am J Epidemiol 130 (5): 1057–1064

    Article  Google Scholar 

  • Woodall WH, Brooke Marshall J, Joner MD Jr, Fraker SE, Abdel-Salam A-SG (2008) On the use and evaluation of prospective scan methods for health-related surveillance. J R Stat Soc Ser A (Stat Soc) 171 (1): 223–237

    MathSciNet  Google Scholar 

  • Wu T-L (2013) On finite Markov chain imbedding and its applications. Methodol Comput Appl Probab 15 (2): 453–465

    Article  MathSciNet  MATH  Google Scholar 

  • Yih WK, Caldwell B, Harmon R, Kleinman K, Lazarus R, Nelson A, Nordin J, Rehm B, Richter B, Ritzwoller D et al (2004) National bioterrorism syndromic surveillance demonstration program. Morb Mortal Weekly Rep 53: 43–49

    Google Scholar 

  • Zhang Z, Assunção R, Kulldorff M (2010) Spatial scan statistics adjusted for multiple clusters. J Probab Stat 2010:1–11

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang T, Zhang Z, Lin G (2012) Spatial scan statistics with overdispersion. Stat Med 31 (8): 762–774

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics and Insurance Science, University of Piraeus, Piraeus, Greece

    Sotiris Bersimis, Athanasios Sachlas & Markos V. Koutras

Authors
  1. Sotiris Bersimis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Athanasios Sachlas
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Markos V. Koutras
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Markos V. Koutras .

Editor information

Editors and Affiliations

  1. University of Connecticut Dept. Statistics, Storrs, CT, USA

    Joseph Glaz

  2. University of Pireaus Dept. Statistics & Insurance Sciences, Piraeus, Greece

    Markos V. Koutras

Section Editor information

  1. Department of Statistics, University of Connecticut, Storrs, CT, USA

    Joseph Glaz

  2. Department of Statistics and Insurance Science, University of Piraeus, Piraeus, Greece

    Markos V. Koutras

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Science+Business Media, LLC, part of Springer Nature

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Bersimis, S., Sachlas, A., Koutras, M.V. (2020). Health Monitoring Techniques Using Scan Statistics. In: Glaz, J., Koutras, M. (eds) Handbook of Scan Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8414-1_54-1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4614-8414-1_54-1

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-8414-1

  • Online ISBN: 978-1-4614-8414-1

  • eBook Packages: Springer Reference MathematicsReference Module Computer Science and Engineering

Publish with us

Policies and ethics

Search

Navigation