Abstract
The scan statistic is widely used in spatial cluster detection applications of inhomogeneous Poisson processes. The most popular variant of the spatial scan is the circular scan. However, such approach has several limitations, in particular, the circular window is not suitable to make the correct description of irregularly shaped and/or unconnected clusters. Additionally, such methodology does not incorporate the tools needed for quantifying the uncertainty in the description of the most likely cluster in the analysis. In the present work we build upon the previously proposed methodology called intensity function a more efficient and accurate way of defining the uncertainty in the identification of spatial clusters using Item Response Theory ideas. Using simulated data we show that the proposed method can correctly identify primary, secondary and irregular clusters.
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References
Balakrishnan N, Koutras MV (2002) Runs and scans with applications. Wiley, New York
Barlow R, Brunk H, Bartholomew D, Bremner J (1972) Statistical Inference Under Order Restrictions: the Theory and Application of Isotonic Regression. Books on Demand, Wiley Series in Probability and Mathematical Statistics
Birnbaum A (1968) Some latent trait models and their use in inferring an examinee’s ability. In: Lord F, Novick M (eds) Statistical theories of mental test scores. Addison-Wesley, Reading, pp 395–479
Boscoe FP, McLaughlin C, Schymura MJ, KielbL CL (2003) Visualization of the spatial scan statistic using nested circles. Health Place 3(9):273–277
Braeken J, Tuerlinckx F (2009) Investigating latent constructs with item response models: a matlab irtm toolbox. Behav Res Methods 41(4):1127–1137
Buckeridge DL, Burkom H, Campbell M, Hogan WR, Moore AW (2005) Algorithms for rapid outbreak detection: a research synthesis. J Biomed Inform 38(2):99–113
Cançado ALF, Duarte AR, Duczmal LH, Ferreira SJ, Fonseca CM (2010) Penalized likelihood and multi-objective spatial scans for the detection and inference of irregular clusters. Int J Health Geogr 55(9):1–17
Chen J, Roth RE, Naito AT, Lengerich EJ, MacEachren AM (2008) Geovisual analytics to enhance spatial scan statistic interpretation: an analysis of U.S. cervical cancer mortality. Int J Health Geogr 7(57):1–18
Conley J, Gahegan M, MacGill J (2005) A genetic approach to detecting clusters in point-data sets. Geogr Anal 37:286–314
Costa M, Kulldorff M (2014) Maximum linkage space-time permutation scan statistics for disease outbreak detection. Int J Health Geogr 13(1):20. doi:10.1186/1476-072X-13-20 http://www.ij-healthgeographics.com/content/13/1/20
Cressie NAC (1993) Statistics for spatial data. Wiley, New York
Duarte AR, Duczmal LH, Ferreira SJ, Cançado ALF (2010) Internal cohesion and geometric shape of spatial clusters. Environ Ecol Stat 17(2):203–229
Duczmal L, Assunção R (2004) A simulated annealing strategy for the detection of arbitrarily shaped spatial clusters. Comput Stat Data Anal 45:269–286
Duczmal L, Cançado ALF, Takahashi RHC, Bessegato LF (2007) A genetic algorithm for irregularly shaped spatial scan statistics. Comput Stat Data Anal 52(1):43–52
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 LH, Cançado ALF, Takahashi RHC (2008) Delineation of irregularly shaped disease clusters through multiobjective optimization. J Comput Graph Stat 17(2):243–262
Duczmal LH, Duarte AR, Tavares R (2009) Extensions of the scan statistic for the detection and inference of spatial clusters. In: Glaz J, Pozdnyakov V, Wallenstein S (eds) Scan statistics: methods and applications. Birkhauser, Boston, pp 153–177
Elliot P, Martuzzi M, Shaddick G (1995) Spatial statistical methods in environmental epidemiology: a critique. Stat Methods Med Res 4(2):137–159
Embretson SE, Reise S (2000) Item response theory for psychologists. Erlbaum Publishers, Mahwah
Glaz J, Naus J, Wallenstein S (2001) Scan statistics. Springer, New York
Goovaerts P (2006) Geostatistical analysis of disease data: visualization and propagation of spatial uncertainty in cancer mortality risk using poisson kriging and p-field simulation. Int J Health Geogr 5(7):1–26
Hardisty F, Conley J (2008) Interactive detection of spatial clusters. Adv Dis Surv 5:37
Jacquez G, Waller L (2000) The effect of uncertain locations on disease cluster statistics. In: Mowrer H, Congalton R (eds) Quantifying spatial uncertainty in natural resources: theory and applications for GIS and remote sensing. CRC, Boca Raton, pp 53–64
Kulldorff M (1997) A spatial scan statistic. Commun Stat 26(6):1481–1496
Kulldorff M (1999) Spatial scan statistics: models, calculations, and applications. In: Glaz J, Balakrishnan M (eds) Scan statistics and applications. Birkhauser, Boston, pp 303–322
Kulldorff M, Nagarwalla N (1995) Spatial disease clusters: detection and inference. Stat Med 14:799–810
Kulldorff M, Tango T, Park PJ (2003) Power comparisons for disease clustering tests. Comput Stat Data Anal 42(4):665–684. doi:10.1016/S0167-9473(02)00160-3 http://www.sciencedirect.com/science/article/pii/S0167947302001603
Kulldorff M, Huang L, Pickle L, Duczmal LH (2006) An elliptic spatial scan statistic. Stat Med 25(22):3929–3943
Lawson A (2001) Statistical methods in spatial epidemiology. Wiley, Chichester
Lawson A (2008) Bayesian disease mapping: hierarchical modeling in spatial epidemiology. CRC Press, Boca Raton
Lawson AB, Boehning D, Lessafre E, Biggeri A, Viel JF, Bertollini R (1999) Disease mapping and risk assessment for public health. Wiley, Chichester
Moore DA, Carpenter TE (1999) Spatial analytical methods and geographic information systems: use in health research and epidemiology. Epidemiol Rev 21(2):143–161
Moreira G, Paquete L, Duczmal L, Menotti D, Takahashi R (2015) Multi-objective dynamic programming for spatial cluster detection. Environ Ecol Stat to appear. doi:10.1007/s10651-014-0302-7
Naus J (1965) The distribution of the size of the maximum cluster of points on a line. J Am Stat Assoc 60:532–538
Neill D (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 74(2):337–360
Oliveira FLP, Duczmal LH, Cançado ALF, Tavares R (2011) Nonparametric intensity bounds for the delineation of spatial clusters. Int J Health Geogr 10:1
Patil GP, Taillie C (2004) Upper level set scan statistic for detecting arbitrarily shaped hotspots. Environ Ecol Stat 11:183–197
Prates MO, Kulldorff M, Assunçao RM (2014) Relative risk estimates from spatial and space-time scan statistics: are they biased? Stat Med 33(15):2634–2644
Rasch G (1960) Probabilistic models for some intelligence and attainment tests. Tech. rep. Danish Institute for Educational Research, Copenhagen
Tango T, Takahashi K (2005) A flexibly shaped spatial scan statistic for detecting clusters. Int J Health Geogr 4:11
Wang T, Yue C (2013) A binary-based approach for detecting irregularly shaped clusters. Int J Health Geogr 12(1):25. doi:10.1186/1476-072X-12-25
Yiannakoulias N, Rosychuk RJ, Hodgson J (2007) Adaptations for finding irregularly shaped disease clusters. Int J Health Geogr 6(28):1–16
Acknowledgments
The authors are deeply indebted to CAPES and to CNPq, Brazil, for financial support via Projects PROCAD-NF 2008 and 459535/2014-5, respectively. Cibele Q. da-Silva and Luiz Duczmal were supported by CNPq-Brazil, BPPesq.
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Cançado, A.L.F., Gomes, A.E., da-Silva, C.Q. et al. An Item Response Theory approach to spatial cluster estimation and visualization. Environ Ecol Stat 23, 435–451 (2016). https://doi.org/10.1007/s10651-016-0347-x
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DOI: https://doi.org/10.1007/s10651-016-0347-x