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Environmental and Ecological Statistics

, Volume 23, Issue 3, pp 435–451 | Cite as

An Item Response Theory approach to spatial cluster estimation and visualization

  • André L. F. Cançado
  • Antonio E. Gomes
  • Cibele Q. da-Silva
  • Fernando L. P. Oliveira
  • Luiz H. Duczmal
Article

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.

Keywords

Inhomogeneous Poisson process Irregularly shaped spatial clusters Item Response Theory Scan statistic Uncertainty 

Notes

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.

References

  1. Balakrishnan N, Koutras MV (2002) Runs and scans with applications. Wiley, New YorkGoogle Scholar
  2. 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 StatisticsGoogle Scholar
  3. 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 395–479Google Scholar
  4. Boscoe FP, McLaughlin C, Schymura MJ, KielbL CL (2003) Visualization of the spatial scan statistic using nested circles. Health Place 3(9):273–277CrossRefGoogle Scholar
  5. Braeken J, Tuerlinckx F (2009) Investigating latent constructs with item response models: a matlab irtm toolbox. Behav Res Methods 41(4):1127–1137CrossRefPubMedGoogle Scholar
  6. Buckeridge DL, Burkom H, Campbell M, Hogan WR, Moore AW (2005) Algorithms for rapid outbreak detection: a research synthesis. J Biomed Inform 38(2):99–113CrossRefPubMedGoogle Scholar
  7. 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):1–17Google Scholar
  8. 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):1–18Google Scholar
  9. Conley J, Gahegan M, MacGill J (2005) A genetic approach to detecting clusters in point-data sets. Geogr Anal 37:286–314CrossRefGoogle Scholar
  10. 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
  11. Cressie NAC (1993) Statistics for spatial data. Wiley, New YorkGoogle Scholar
  12. Duarte AR, Duczmal LH, Ferreira SJ, Cançado ALF (2010) Internal cohesion and geometric shape of spatial clusters. Environ Ecol Stat 17(2):203–229CrossRefGoogle Scholar
  13. Duczmal L, Assunção R (2004) A simulated annealing strategy for the detection of arbitrarily shaped spatial clusters. Comput Stat Data Anal 45:269–286CrossRefGoogle Scholar
  14. Duczmal L, Cançado ALF, Takahashi RHC, Bessegato LF (2007) A genetic algorithm for irregularly shaped spatial scan statistics. Comput Stat Data Anal 52(1):43–52CrossRefGoogle Scholar
  15. Duczmal LH, Kulldorff M, Huang L (2006) Evaluation of spatial scan statistics for irregularly shaped clusters. J Comput Graph Stat 15(2):428–442CrossRefGoogle Scholar
  16. Duczmal LH, Cançado ALF, Takahashi RHC (2008) Delineation of irregularly shaped disease clusters through multiobjective optimization. J Comput Graph Stat 17(2):243–262CrossRefGoogle Scholar
  17. 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 153–177Google Scholar
  18. Elliot P, Martuzzi M, Shaddick G (1995) Spatial statistical methods in environmental epidemiology: a critique. Stat Methods Med Res 4(2):137–159CrossRefGoogle Scholar
  19. Embretson SE, Reise S (2000) Item response theory for psychologists. Erlbaum Publishers, MahwahGoogle Scholar
  20. Glaz J, Naus J, Wallenstein S (2001) Scan statistics. Springer, New YorkCrossRefGoogle Scholar
  21. 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):1–26Google Scholar
  22. Hardisty F, Conley J (2008) Interactive detection of spatial clusters. Adv Dis Surv 5:37Google Scholar
  23. 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 53–64Google Scholar
  24. Kulldorff M (1997) A spatial scan statistic. Commun Stat 26(6):1481–1496CrossRefGoogle Scholar
  25. Kulldorff M (1999) Spatial scan statistics: models, calculations, and applications. In: Glaz J, Balakrishnan M (eds) Scan statistics and applications. Birkhauser, Boston, pp 303–322CrossRefGoogle Scholar
  26. Kulldorff M, Nagarwalla N (1995) Spatial disease clusters: detection and inference. Stat Med 14:799–810CrossRefPubMedGoogle Scholar
  27. 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
  28. Kulldorff M, Huang L, Pickle L, Duczmal LH (2006) An elliptic spatial scan statistic. Stat Med 25(22):3929–3943CrossRefPubMedGoogle Scholar
  29. Lawson A (2001) Statistical methods in spatial epidemiology. Wiley, ChichesterGoogle Scholar
  30. Lawson A (2008) Bayesian disease mapping: hierarchical modeling in spatial epidemiology. CRC Press, Boca RatonCrossRefGoogle Scholar
  31. Lawson AB, Boehning D, Lessafre E, Biggeri A, Viel JF, Bertollini R (1999) Disease mapping and risk assessment for public health. Wiley, ChichesterGoogle Scholar
  32. Moore DA, Carpenter TE (1999) Spatial analytical methods and geographic information systems: use in health research and epidemiology. Epidemiol Rev 21(2):143–161CrossRefPubMedGoogle Scholar
  33. 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
  34. Naus J (1965) The distribution of the size of the maximum cluster of points on a line. J Am Stat Assoc 60:532–538CrossRefGoogle Scholar
  35. Neill D (2011) Fast bayesian scan statistics for multivariate event detection and visualization. Stat Med 30(5):455–469CrossRefPubMedGoogle Scholar
  36. Neill DB (2012) Fast subset scan for spatial pattern detection. J R Stat Soc 74(2):337–360CrossRefGoogle Scholar
  37. Oliveira FLP, Duczmal LH, Cançado ALF, Tavares R (2011) Nonparametric intensity bounds for the delineation of spatial clusters. Int J Health Geogr 10:1CrossRefPubMedPubMedCentralGoogle Scholar
  38. Patil GP, Taillie C (2004) Upper level set scan statistic for detecting arbitrarily shaped hotspots. Environ Ecol Stat 11:183–197CrossRefGoogle Scholar
  39. Prates MO, Kulldorff M, Assunçao RM (2014) Relative risk estimates from spatial and space-time scan statistics: are they biased? Stat Med 33(15):2634–2644CrossRefPubMedPubMedCentralGoogle Scholar
  40. Rasch G (1960) Probabilistic models for some intelligence and attainment tests. Tech. rep. Danish Institute for Educational Research, CopenhagenGoogle Scholar
  41. Tango T, Takahashi K (2005) A flexibly shaped spatial scan statistic for detecting clusters. Int J Health Geogr 4:11Google Scholar
  42. 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 CrossRefPubMedPubMedCentralGoogle Scholar
  43. Yiannakoulias N, Rosychuk RJ, Hodgson J (2007) Adaptations for finding irregularly shaped disease clusters. Int J Health Geogr 6(28):1–16Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • André L. F. Cançado
    • 1
  • Antonio E. Gomes
    • 1
  • Cibele Q. da-Silva
    • 1
  • Fernando L. P. Oliveira
    • 2
  • Luiz H. Duczmal
    • 3
  1. 1.Statistics DepartmentUniversidade de BrasıliaBrasıliaBrazil
  2. 2.Statistics DepartmentUniversidade Federal de Ouro PretoOuro PretoBrazil
  3. 3.Statistics DepartmentUniversidade Federal de Minas GeraisBelo HorizonteBrazil

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