An investigation of the impact of various geographical scales for the specification of spatial dependence

References

• P. Adhikari, Socio-economic Indexes for Areas: Introduction, Use and Future Directions, Australian Bureau of Statistics, Canberra, Australian Capital Territory, 2006.
   Google Scholar
• AIHW, Rural, Regional and Remote Health: A Guide to Remoteness Classifications, Australian Institute of Health and Welfare AIHW Cat. No. PHE 53, Canberra, 2004.
   Google Scholar
• L. Anselin, I. Syabri, and Y. Kho, GeoDa: An introduction to spatial data analysis, Geogr. Anal. 38 (2006), pp. 5–22. doi: 10.1111/j.0016-7363.2005.00671.x
   Web of Science ®Google Scholar
• R. Assunção and E. Krainski, Neighborhood dependence in Bayesian spatial models, Biom. J. 51 (2009), pp. 851–869. doi: 10.1002/bimj.200900056
   PubMed Web of Science ®Google Scholar
• P.D. Baade, G. Turrell, and J.F. Aitken, Geographic remoteness, area-level socio-economic disadvantage and advanced breast cancer: A cross-sectional, multilevel study, J. Epidemiol. Community Health 65 (2011), pp. 1037–1043. doi: 10.1136/jech.2010.114777
   PubMed Web of Science ®Google Scholar
• S. Banerjee, B.P. Carlin, and A.E. Gelfand, Hierarchical Modeling and Analysis for Spatial Data, Vol. 101, Chapman & Hall/CRC, Boca Raton, FL, 2004.
   Google Scholar
• L. Bernardinelli, D. Clayton, and C. Montomoli, Bayesian estimates of disease maps: How important are priors? Stat. Med. 14 (1995), pp. 2411–2431. doi: 10.1002/sim.4780142111
   PubMed Web of Science ®Google Scholar
• J. Besag and C. Kooperberg, On conditional and intrinsic autoregressions, Biometrika 82 (1995), pp. 733–746.
   Web of Science ®Google Scholar
• J. Besag, J. York, and A. Mollié, Bayesian image restoration, with two applications in spatial statistics, Ann. Inst. Statist. Math. 43 (1991), pp. 1–59. doi: 10.1007/BF00116466
   Web of Science ®Google Scholar
• N. Best, S. Cockings, J. Bennett, J. Wakefield, and P. Elliott, Ecological regression analysis of environmental benzene exposure and childhood leukaemia: Sensitivity to data inaccuracies, geographical scale and ecological bias, J. Roy. Statist. Soc. Ser. A 164 (2001), pp. 155–174. doi: 10.1111/1467-985X.00194
   Google Scholar
• R. Bivand, L. Anselin, O. Berke, A. Bernat, M. Carvalho, Y. Chun, C.F. Dormann, S. Dray, R. Halbersma, and N. Lewin-Koh, spdep: Spatial Dependence: Weighting Schemes, Statistics and Models, R Package Version 0.5-56, 2011. Available at http://cran.r-project.org/web/packages/spdep/index.html.
   Google Scholar
• M. Blangiardo, M. Cameletti, G. Baio, and H. Rue, Spatial and spatio-temporal models with R-INLA, Spat. Spatiotemporal Epidemiol. 4 (2013), pp. 33–49. doi: 10.1016/j.sste.2012.12.001
   PubMedGoogle Scholar
• N. Cressie, Statistics for Spatial Data, John Wiley and Sons, Inc, New York, 1993.
   Google Scholar
• N. Cressie and N.H. Chan, Spatial modeling of regional variables, J. Amer. Statist. Assoc. 84 (1989), pp. 393–401. doi: 10.1080/01621459.1989.10478783
   Web of Science ®Google Scholar
• W.R. Gilks, S. Richardson, and D.J. Spiegelhalter, Markov Chain Monte Carlo in Practice: Interdisciplinary Statistics, Vol. 2, Chapman & Hall/CRC, London, 1995.
   Google Scholar
• A.N. Glynn and J. Wakefield, Ecological inference in the social sciences, Stat. Med. 7 (2010), pp. 307–322.
   Google Scholar
• T. Gneiting and A.E. Raftery, Strictly proper scoring rules, prediction, and estimation, J. Amer. Statist. Assoc. 102 (2007), pp. 359–378. doi: 10.1198/016214506000001437
   Web of Science ®Google Scholar
• L.A. Goodman, Ecological regressions and behaviour of individuals, Amer. Sociol. Rev. 18 (1953), pp. 663–664. doi: 10.2307/2088121
   Web of Science ®Google Scholar
• L.A. Goodman, Some alternatives to ecological correlation, Amer. J. Sociol. 64 (1959), pp. 610–625. doi: 10.1086/222597
   Web of Science ®Google Scholar
• P. Goovaerts, Combining area-based and individual-level data in the geostatistical mapping of late-stage cancer incidence, Spat. Spatiotemporal Epidemiol. 1 (2009), pp. 61–71. doi: 10.1016/j.sste.2009.07.001
   Google Scholar
• P.J. Green, A primer on Markov chain Monte Carlo, in Complex Stochastic Systems, O.E. Barndorff-Nielsen, D.R. Cox, and K. Kluppelberg, eds., Chapman & Hall, London, 2001, pp. 1–62.
   Google Scholar
• S. Greenland, Ecologic versus individual-level sources of bias in ecologic estimates of contextual health effects, Int. J. Epidemiol. 30 (2001), pp. 1343–1350. doi: 10.1093/ije/30.6.1343
   PubMed Web of Science ®Google Scholar
• S. Greenland, A review of multilevel theory for ecologic analyses, Stat. Med. 21 (2002), pp. 389–395. doi: 10.1002/sim.1024
   PubMed Web of Science ®Google Scholar
• S. Haneuse and J. Wakefield, Geographic-based ecological correlation studies using supplemental case-control data, Stat. Med. 27 (2008), pp. 864–887. doi: 10.1002/sim.2979
   PubMed Web of Science ®Google Scholar
• S.J. Haneuse and J.C. Wakefield, Hierarchical models for combining ecological and case-control data, Biometrics 63 (2007), pp. 128–136. doi: 10.1111/j.1541-0420.2006.00673.x
   PubMed Web of Science ®Google Scholar
• S.J. Haneuse and J.C. Wakefield, The combination of ecological and case-control data, J. R. Stat. Soc. Ser. B Stat. Methodol. 70 (2008), pp. 73–93. doi: 10.1111/j.1467-9868.2007.00628.x
   PubMedGoogle Scholar
• M. Haran, Gaussian random field models for spatial data, in Handbook of Markov Chain Monte Carlo, S.P. Brooks et al., eds., CRC Press, Boca Raton, 2011, pp. 449–478.
   Google Scholar
• C. Jackson, N. Best, and S. Richardson, Improving ecological inference using individual-level data, Stat. Med. 25 (2006), pp. 2136–2159. doi: 10.1002/sim.2370
   PubMed Web of Science ®Google Scholar
• C. Jackson, N. Best, and S. Richardson, Hierarchical related regression for combining aggregate and individual data in studies of socio-economic disease risk factors, J. Roy. Statist. Soc. Ser. A 171 (2008), pp. 159–178.
   Google Scholar
• R. Johnston and C. Pattie, Ecological inference and entropy-maximizing: An alternative estimation procedure for split-ticket voting, Political Anal. 8 (2000), pp. 333–345. doi: 10.1093/oxfordjournals.pan.a029819
   Google Scholar
• G. King, A Solution to the Ecological Inference Problem, Princeton University Press, Princeton, NJ, 1997.
   Google Scholar
• G. King, Geography, statistics, and ecological inference, Ann. Assoc. Am. Geogr. 90 (2004), pp. 601–606. doi: 10.1111/0004-5608.00214
   Web of Science ®Google Scholar
• L. Knorr-Held, Bayesian modelling of inseparable space-time variation in disease risk, Stat. Med. 19 (2000), pp. 2555–2567. doi: 10.1002/1097-0258(20000915/30)19:17/18<2555::AID-SIM587>3.0.CO;2-#
   PubMed Web of Science ®Google Scholar
• L. Knorr-Held and J. Besag, Modelling risk from a disease in time and space, Stat. Med. 17 (1998), pp. 2045–2060. doi: 10.1002/(SICI)1097-0258(19980930)17:18<2045::AID-SIM943>3.0.CO;2-P
   PubMed Web of Science ®Google Scholar
• L.I. Langbein and A.J. Lichtman, Ecological Inference, Series/No. 07-010, Sage, Thousand Oaks, CA, 1978.
   Google Scholar
• A.B. Lawson and H.R. Song, Bayesian hierarchical modeling of the dynamics of spatio-temporal influenza season outbreaks, Spat. Spatiotemporal Epidemiol. 1 (2010), pp. 187–195. doi: 10.1016/j.sste.2010.03.001
   Google Scholar
• D. Lee, A comparison of conditional autoregressive models used in Bayesian disease mapping, Spat. Spatiotemporal Epidemiol. 2 (2011), pp. 79–89. doi: 10.1016/j.sste.2011.03.001
   PubMedGoogle Scholar
• F. Lindgren, H. Rue, and J. Lindström, An explicit link between Gaussian fields and Gaussian Markov random fields: The stochastic partial differential equation approach, J. R. Stat. Soc. Ser. B Stat. Methodol. 73 (2011), pp. 423–498. doi: 10.1111/j.1467-9868.2011.00777.x
   Web of Science ®Google Scholar
• S. Martino and H. Rue, Case studies in Bayesian computation using INLA, in Complex Data Modeling and Computationally Intensive Statistical Methods, P. Mantovan and P. Secchi, eds., Springer-Verlag, Milan, Italy, 2010, pp. 99–114.
   Google Scholar
• X. Min, D. Sun, Z. He, and M. Schootman, A Bayesian hierarchical model of nontraumatic lower-extremity amputation rates, Spat. Spatiotemporal Epidemiol. 1 (2010), pp. 169–76. doi: 10.1016/j.sste.2010.03.008
   Google Scholar
• H. Morgenstern, Ecologic studies in epidemiology: Concepts, principles, and methods, Annu. Rev. Publ. Health 16 (1995), pp. 61–81. doi: 10.1146/annurev.pu.16.050195.000425
   PubMed Web of Science ®Google Scholar
• S. Openshaw, Concepts and Techniques in Modern Geography Number 38: The Modifiable Areal Unit Problem, Geo Books, Norwich, 1984.
   Google Scholar
• S. Openshaw and P. Taylor, A million or 80 correlation coefficient: Three experiments on the modifiable areal unit problem, in Statistical Applications in the Spatial Sciences, N. Wrigley, ed., Pion Press, London, 1979, pp. 127–144.
   Google Scholar
• E.J. Pebesma, Multivariable geostatistics in S: The gstat package, Comput. Geosci. 30 (2004), pp. 683–691. doi: 10.1016/j.cageo.2004.03.012
   Web of Science ®Google Scholar
• J.N. Perry, A.M. Liebhold, M.S. Rosenberg, J. Dungan, M. Miriti, A. Jakomulska, and S. Citron-Pousty, Illustrations and guidelines for selecting statistical methods for quantifying spatial pattern in ecological data, Ecography 25 (2002), pp. 578–600. doi: 10.1034/j.1600-0587.2002.250507.x
   Web of Science ®Google Scholar
• R.L. Prentice and L. Sheppard, Aggregate data studies of disease risk factors, Biometrika 82 (1995), pp. 113–125. doi: 10.1093/biomet/82.1.113
   Web of Science ®Google Scholar
• S. Richardson and N. Best, Bayesian hierarchical models in ecological studies of health-environment effects, Environmetrics 14 (2003), pp. 129–147. doi: 10.1002/env.571
   Web of Science ®Google Scholar
• W.S. Robinson, Ecological correlations and the behavior of individuals, Int. J. Epidemiol. 38 (2009), pp. 337–341. doi: 10.1093/ije/dyn357
   PubMed Web of Science ®Google Scholar
• H. Rue and S. Martino, Approximate Bayesian inference for hierarchical Gaussian Markov random field models, J. Statist. Plann. Inference 137 (2007), pp. 3177–3192. doi: 10.1016/j.jspi.2006.07.016
   Web of Science ®Google Scholar
• H. Rue, S. Martino, and N. Chopin, Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations, J. R. Stat. Soc. Ser. B Stat. Methodol. 71 (2009), pp. 319–392. doi: 10.1111/j.1467-9868.2008.00700.x
   Web of Science ®Google Scholar
• R. Salway and J. Wakefield, Sources of bias in ecological studies of non-rare events, Environ. Ecol. Stat. 12 (2005), pp. 321–347. doi: 10.1007/s10651-005-1516-5
   Web of Science ®Google Scholar
• H.C. Selvin, Durkheim's suicide and problems of empirical research, Amer. J. Sociol. 63 (1958), pp. 607–619. doi: 10.1086/222356
   Web of Science ®Google Scholar
• H.R. Song, A. Lawson, R.B. D'Agostino, and A.D. Liese, Modeling type 1 and type 2 diabetes mellitus incidence in youth: An application of Bayesian hierarchical regression for sparse small area data, Spat. Spatiotemporal Epidemiol. 2 (2011), pp. 23–33. doi: 10.1016/j.sste.2010.09.008
   Google Scholar
• D.J. Spiegelhalter, N.G. Best, B.P. Carlin, and A.V.D. Linde, Bayesian measures of model complexity and fit, J. R. Stat. Soc. Ser. B Stat. Methodol. 64 (2002), pp. 583–639. doi: 10.1111/1467-9868.00353
   Web of Science ®Google Scholar
• M.L. Stein, Interpolation of Spatial Data: Some Theory for Kriging, Chapter 2, Springer Verlag, New York, 1999.
   Google Scholar
• L. Tierney and J.B. Kadane, Accurate approximations for posterior moments and marginal densities, J. Amer. Statist. Assoc. 81 (1986), pp. 82–86. doi: 10.1080/01621459.1986.10478240
   Web of Science ®Google Scholar
• J. Wakefield, Sensitivity analyses for ecological regression, Biometrics 59 (2003), pp. 9–17. doi: 10.1111/1541-0420.00002
   PubMed Web of Science ®Google Scholar
• J. Wakefield, Ecological inference for 2×2 tables (with discussion), J. Roy. Statist. Soc. Ser. A 167 (2004), pp. 385–445. doi: 10.1111/j.1467-985x.2004.02046_1.x
   Google Scholar
• J. Wakefield, Disease mapping and spatial regression with count data, Biostatistics 8 (2007), pp. 158–183. doi: 10.1093/biostatistics/kxl008
   PubMed Web of Science ®Google Scholar
• J. Wakefield, Ecologic studies revisited, Annu. Rev. Publ. Health 29 (2008), pp. 75–90. doi: 10.1146/annurev.publhealth.29.020907.090821
   PubMed Web of Science ®Google Scholar
• J. Wakefield, Multi-level modelling, the ecologic fallacy, and hybrid study designs, Int. J. Epidemiol. 38 (2009), pp. 330–336. doi: 10.1093/ije/dyp179
   PubMed Web of Science ®Google Scholar
• J. Wakefield and R. Salway, A statistical framework for ecological and aggregate studies, J. Roy. Statist. Soc. Ser. A 164 (2001), pp. 119–137. doi: 10.1111/1467-985X.00191
   Google Scholar
• J.C. Wakefield, N.G. Best, and L. Waller, Bayesian approaches to disease mapping, in Spatial Epidemiology: Methods and Applications, P. Elliott et al., eds., Oxford University Press, Oxford, 2000, pp. 99–114.
   Google Scholar
• L. Waller and B. Carlin, Disease mapping, in Handbook of Spatial Statistics, A.E. Gelfand et al., eds., CRC Press, Boca Raton, FL, 2010, pp. 217–244.
   Google Scholar