Abstract
This work presents a methodology to detect space-time clusters, based on adaptive likelihood ratios (ALRs), which preserves the martingale structure of the regular likelihood ratio. Monte Carlo simulations are not required to validate the procedure’s statistical significance, because the upper limit for the false alarm rate of the proposed method depends only on the quantity of evaluated cluster candidates, thus allowing the construction of a fast computational algorithm. The quantity of evaluated clusters is also significantly reduced, by using another adaptive scheme to prune many unpromising clusters, further increasing the computational speed. Performance is evaluated through simulations to measure the average detection delay and the probability of correct cluster detection. Applications for thyroid cancer in New Mexico and hanseniasis in children in the Brazilian Amazon are shown.
Similar content being viewed by others
References
Cançado A, Duarte A, Duczmal L, Ferreira S, Fonseca C, Gontijo E (2010) Penalized likelihood and multi-objective spatial scans for the detection and inference of irregular clusters. Int J Health Geogr 9:55
Duarte A, Cançado A, Duczmal L, Ferreira S (2010) Internal cohesion and geometric shape of spatial clusters. Environ Ecol Stat 17:203–229
Duczmal LH, Assunção RM (2004) A simulated annealing strategy for the detection of arbitrary shaped spatial clusters. Comput Stat Data Anal 45:269–286
Duczmal L, Buckeridge DL (2006) A workflow spatial scan statistic. Stat Med 25:743–754
Duczmal LH, Kulldorff M, Huang L (2006) Evaluation of spatial scan statistics for irregularly shaped clusters. J Comput Graph Stat 15(2):428–442
Duczmal L, Cançado AL, Takahashi RH, Bessegato LF (2007) A genetic algorithm for irregularly shaped spatial scan statistics. Comput Stat Data Anal 52:43–52
Duczmal LH, Cançado ALF, Takahashi RHC (2008) Geographic delineation of disease clusters through multi-objective optimization. J Comput Graph Stat 17:243–262
Duczmal L, Duarte AR, Tavares R (2009) Extensions of the scan statistic for the detection and inference of spatial clusters. In: Balakrishnan N, Glaz J (eds) Scan statistics. Birkhäuser, Basel. pp 157–182
Duczmal LH, Moreira GJP, Burgarelli D, Takahashi RHC, Magalhães FCO, Bodevan EC (2011) Voronoi distance based prospective space-time scans for point data sets: a dengue fever cluster analysis in a southeast Brazilian town. Int J Health Geogr 10:29
Krieger AM, Moshe Pollak M, Yakir B (2003) Surveillance of a simple linear regression. JASA 98(462):456–469
Kulldorff M (1997) A spatial scan statistic. Commun Stat Theory Methods 26:1481–1496
Kulldorff M (2001) Prospective time periodic geographical disease surveillance using a scan statistic. J R Stat Soc A 164:61–72
Kulldorff M, Huang L, Pickle L, Duczmal L (2006) An elliptic spatial scan statistic. Stat Med 25:3929–3943
Lai TL (1995) Sequential change point detection in quality control and dynamical systems. J R Stat Soc A 57:613–658
Lima MS (2011) Adaptive methods for the detection of space-time clusters. Ph.D. thesis, Universidade Federal de Minas Gerais
Lima MS, Duczmal LH (2009) Endemic disease surveillance using Bayes factor. In: International society for disease surveillance eighth annual conference, Miami, EUA
Lima MS, Duczmal LH (2012) Surveillance and detection of space-time clusters using adaptive Bayes factor. In: Bradley DG (eds) Cancer clusters. Series: cancer etiology, diagnosis and treatments. Nova Science Publishers. ISBN:978-1-61209-516-5
Lima MS, Duczmal LH (2014) Adaptive likelihood ratio approaches for the detection of space-time disease clusters. Comput Stat Data Anal 77:352–370
Lorden G, Pollak M (2005) Non-anticipating estimation applied to sequential analysis and change-point detection. Ann Stat 33:1422–1454
Marshall JB, Spitzner DJ, Woodall WH (2007) Use of the local knox statistic for prospective monitoring of disease occurrences in space and time. Stat Med 26:1576–1593
Neill DB (2009) Expectation-based scan statistics for monitoring space-time clusters. Int J Forecast 25:498–517
Neill DB (2011) Fast Bayesian scan statistics for multivariate event detection and visualization. Stat Med 30(5):455–469
Neill DB (2012) Fast subset scan for spatial pattern detection. J R Stat Soc B 74(2):337–360
Page ES (1954) Continuous inspection schemes. Biometrika 41:100–115
Patil GP, Taillie C (2004) Upper level set scan statistic for detecting arbitrarily shaped hotspots. Environ Ecol Stat 11:183–197
Pavlov IV (2003) Sequential procedure of testing composite hypotheses with applications to the Kiefer-Weiss. Theory Prob Appl 35:280–292
Pollak M (1987) Average run lengths of an optimal method of detecting a change in distribution. Ann Stat 15:749–779
Porter DM (2007) Some adaptive approaches for space-time anomaly detection. In: First international workshop in sequential methodologies, IWSM, Boulder
Roberts SW (1966) A comparison of some control chart procedures. Technometrics 8:411–430
Rogerson PA (2001) Monitoring point patterns for the development of space-time clusters. J R Stat Soc A 164:87–96
Sonesson C (2007) A CUSUM framework for detection of space time disease clusters using scan statistic. Stat Med 26:4770–4789
Takahashi K, Kulldorff M, Tango T, Yin K (2008) A flexibly shaped space-time scan statistic for disease outbreak detection and monitoring. Int J Health Geogr 7:14
Tango T, Takahashi K (2005) A flexibly shaped spatial scan statistic for detecting clusters. Int J Health Geogr 4:11
Tango T, Takahashi K, Kohriyama K (2011) A space-time scan statistic for detecting emerging outbreaks. Biometrics 4:1–10
Tartakovsky AG, Rozovskii LR, Blazek RB, Kim H (2006) Detection of intrusions in information systems by sequential change-point methods. Stat Methodol 3:252–293
West, M (1986) Bayesian model monitoring. J R Stat Soc B 48:70–78
Yiannakoulias N, Rosychuk R, Hodgson J (2007) Adaptations for finding irregularly shaped disease clusters. Int J Health Geograp 6:28
Acknowledgements
The authors were funded with grants from the Brazilian agencies CAPES, UFAM, CNPq, and FAPEMIG.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Section Editor information
Rights and permissions
Copyright information
© 2017 Springer Science+Business Media LLC
About this entry
Cite this entry
deLima, M.S., Duczmal, L.H. (2017). Adaptive Likelihood Ratio Scans for the Detection of Space-Time Clusters. In: Glaz, J., Koutras, M. (eds) Handbook of Scan Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8414-1_37-1
Download citation
DOI: https://doi.org/10.1007/978-1-4614-8414-1_37-1
Received:
Accepted:
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