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Exploring the Specifications of Spatial Adjacencies and Weights in Bayesian Spatial Modeling with Intrinsic Conditional Autoregressive Priors in a Small-area Study of Fall Injuries

School of Public Health and Health Systems, University of Waterloo, ON, Canada

Special Issues: Spatial Aspects of Health: Methods and Applications

Intrinsic conditional autoregressive modeling in a Bayeisan hierarchical framework has been increasingly applied in small-area ecological studies. This study explores the specifications of spatial structure in this Bayesian framework in two aspects: adjacency, i.e., the set of neighbor(s) for each area; and (spatial) weight for each pair of neighbors. Our analysis was based on a small-area study of falling injuries among people age 65 and older in Ontario, Canada, that was aimed to estimate risks and identify risk factors of such falls. In the case study, we observed incorrect adjacencies information caused by deficiencies in the digital map itself. Further, when equal weights was replaced by weights based on a variable of expected count, the range of estimated risks increased, the number of areas with probability of estimated risk greater than one at different probability thresholds increased, and model fit improved. More importantly, significance of a risk factor diminished. Further research to thoroughly investigate different methods of variable weights; quantify the influence of specifications of spatial weights; and develop strategies for better defining spatial structure of a map in small-area analysis in Bayesian hierarchical spatial modeling is recommended.
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Keywords spatial structure; variable weights; equal weights; adjacent matrix; Bayesian; spatial epidemiology; WinBUGS; neighbourhood structure

Citation: Jane Law. Exploring the Specifications of Spatial Adjacencies and Weights in Bayesian Spatial Modeling with Intrinsic Conditional Autoregressive Priors in a Small-area Study of Fall Injuries. AIMS Public Health , 2016, 3(1): 65-82. doi: 10.3934/publichealth.2016.1.65


  • 1. Besag J, York J, Mollie A (1991) Bayesian image restoration with two applications in spatial statistics. Annals Institute Stat Mathe 43: 1-59.    
  • 2. Congdon P (2003) Applied Bayesian Modelling. Chichester: John Wiley, 276-281.
  • 3. Graham P (2008) Intelligent smoothing using hierarchical Bayesian models. Epidemiology 19: 493-495.    
  • 4. Ryan L (2009) Spatial epidemiology: some pitfalls and opportunities. Epidemiology 20: 242-244.    
  • 5. Waller LA, Gotway CA (2004) Applied spatial statistics for public health data. Hoboken, N.J.: John Wiley & Sons, 259-260.
  • 6. Conlon EM, Waller LA (1998) Flexible neighborhood structures in hierarchical models for disease mapping. University of Minnesota Biostatistics Research Report, No rr98-018: Division of Biostatistics, University of Minnesota.
  • 7. Lee D, Mitchell R (2012) Boundary detection in disease mapping studies. Biostatistics 13: 415-426.    
  • 8. Lu H, Reilly CS, Banerjee S, et al. (2007) Bayesian areal wombling via adjacency modeling. EnvirEcolog Stat 14: 433-452.
  • 9. Ma H, Carlin BP (2007) Bayesian multivariate areal wombling for multiple disease boundary analysis. Bayesian analysis 2: 281-302.    
  • 10. Lee D, Rushworth A, Sahu SK (2014) A Bayesian localized conditional autoregressive model for estimating the health effects of air pollution. Biometrics 70: 419-429.    
  • 11. Chan WC, Law J, Seliske P (2012) Bayesian spatial methods for small-area injury analysis: a study of geographical variation of falls in older people in the Wellington-Dufferin-Guelph health region of Ontario, Canada. Injury Preve 18: 303-308.    
  • 12. Ministry of Health and Long-term Care. Fall-Related Hospitalizations Among Seniors, 2011. Available from http://www.health.gov.on.ca/english/public/pub/pubhealth/init_report/fhas.html.
  • 13. Congdon P (2006) Bayesian Statistical Modelling, Second Edition. Chichester: John Wiley, 303-310.
  • 14. Law J, Haining RP (2004) A Bayesian Approach to Modelling Binary Data: the Case of High-intensity Crime Areas. Geog Analysis 36: 197-216.    
  • 15. Kelsall JE, Wakefield JC (1999) Discussion of 'Bayesian models for spatially correlated disease and exposure data' by Best et al. In: Bernardo JM, Berger JO, David AP et al., editors. Bayesian Statistics 6: Oxford University Press. pp. 151.
  • 16. U.S. Geological Survey Adjacency for WinBUGS tool, 2015. Available from http://www.umesc.usgs.gov/management/dss/adjacency_tool.html.
  • 17. Law J, Quick M (2013) Exploring links between juvenile offenders and social disorganization at a large map scale: a Bayesian spatial modeling approach. J Geog Sys 15: 89-113.    
  • 18. Spiegelhalter DJ, Best N, Carlin BP, et al. (2001) Bayesian measures of model complexity and fit. Medical Research Council Biostatistics Unit, Cambridge, UK.
  • 19. Best N, Arnold R, Thomas A, et al. (1999) Bayesian models for spatially correlated disease and exposure data. In: Bernardo JM, Berger JO, David AP et al., editors. Bayesian Statistics 6. Oxford: Oxford University Press. pp. 131-156.
  • 20. Assuncao R, Krainski E (2009) Neighborhood dependence in Bayesian spatial models. Biometrical J 51: 851-869.    


This article has been cited by

  • 1. Earl W. Duncan, Kerrie L. Mengersen, Qiang Zeng, Comparing Bayesian spatial models: Goodness-of-smoothing criteria for assessing under- and over-smoothing, PLOS ONE, 2020, 15, 5, e0233019, 10.1371/journal.pone.0233019

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