A spatial beta-binomial model for clustered count data on dental caries

Statistical Methods in Medical Research

Volumn 20, Issue 2, 2011, Pages 85-102

  Bandyopadhyay, Dipankar ^a,c   Reich, Brian J ^b   Slate, Elizabeth H ^a  

^a MEDICAL UNIVERSITY OF SOUTH CAROLINA   (United States)

^b NORTH CAROLINA STATE UNIVERSITY   (United States)

^c MEDICAL UNIVERSITY OF SOUTH CAROLINA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; BAYES THEOREM; BETA BINOMIAL MODEL; DATA ANALYSIS; DENTAL CARIES; HUMAN; PREVALENCE; REGRESSION ANALYSIS; SPATIAL AUTOCORRELATION ANALYSIS; STATISTICAL ANALYSIS; VARIANCE;

BAYES THEOREM; BIOSTATISTICS; DATA INTERPRETATION, STATISTICAL; DENTAL CARIES; HUMANS; LIKELIHOOD FUNCTIONS; MODELS, STATISTICAL; MULTIVARIATE ANALYSIS;

EID: 79955687606     PISSN: 09622802     EISSN: None     Source Type: Journal    
DOI: 10.1177/0962280210372453     Document Type: Article

References (45)

1. US Department of Health and Human Services, Oral Health in America. A report of the Surgeon General, National Institutes of Dental and Craniofacial Research, National Institutes of Health 2000: 1-308.
2. Fejerskov O, Kidd EAM, eds. Dental caries: the disease and its clinical management. Blackwell, Copenhagen ; 2003.
3. Kidd EA, Giedrys-Leeper E., Simons D. Take two dentists: a tale of root caries. Dental Update 2000 ; 27: 222-30.
4. World Health Organization. The world oral health report 2003. WHO, Geneva ; 2003.
5. Curzon ME, Preston AJ Risk groups: nursing bottle caries/caries in the elderly. Caries Research 2004 ; 38 (suppl 1). 24-33. (Pubitemid 38056701)
6. Petersen PE, Yamamoto T. Improving the oral health care of older people: the approach of the WHO global oral health programme. Community Dentistry and Oral Epidemiology 2005 ; 33: 81-92. (Pubitemid 41577044)
7. Vieira AR, Marazita ML, Goldstein-McHenry T. Genome-wide scan finds suggestive caries loci. Journal of Dental Research 2008 ; 87 (5). 435-9.
8. Keyes PH The infectious and transmissible nature of experimental dental caries: findings and Implications. Archives of Oral Biology 1960 ; 13: 304-20.
9. Keyes PH Recent advances in dental caries research. International Dentistry Journal 1962 ; 12: 443-63.
10. Selwitz RH, Ismail AI, Pitts NB Dental caries. Lancet 2007 ; 369: 51-9. (Pubitemid 46027228)
11. Fernandes J., Slate EH, Wiegand RE, et al. Dental caries in Type 2 Gullah diabetics, Journal of Dental Research 2007 ; 86 (Special Issue A): 1054 ( www.dentalresearch.org ).
12. Burnside G., Pine CM, Williamson PR The application of multilevel modelling to dental caries data. Statistics in Medicine 2007 ; 26: 4139-49. (Pubitemid 47399344)
13. Darby ML, Walsh MM Dental hygiene: theory and practice (2nd edn). W. B. Saunders Company, USA; 2003.
14. Williams DA The analysis of binary responses from toxicological experiments involving reproduction and teratogenicity. Biometrics 1975 ; 31: 949-52.
15. Williams DA Extra-binomial variation in logistic linear models. Applied Statistics 1982 ; 31: 144-8.
16. Lawson AB Bayesian disease mapping: hierarchical modeling in spatial epidemiology. CRC Press, Boca Raton, FL ; 2009.
17. Griffiths DA Maximum likelihood estimation of the betabinomial distribution and an application to the household incidence of the total number of cases of a disease, Biometrics 1973 ; 29: 637-48.
18. Prentice RL Binary regression using an extended betabinomial distribution with discussion of correlation induced by covariate measurement errors. Journal of the American Statistical Association 1986 ; 81: 321-7.
19. Ainsworth L. Models and methods for spatial data: detecting outliers and handling zero-inflated counts. PhD dissertation, Simon Fraser University, Burnaby (BC, Canada); 2007.
20. Besag J. Spatial interaction and the statistical analysis of lattice systems (with discussion), Journal of the Royal Statistical Society, Series B 1974 ; 36: 192-236.
21. Mardia KV Multidimensional multivariate Gaussian Markov random fields with applications to image processing. Journal of Multivariate Analysis 1998 ; 24: 45-64.
22. Lawson AB, Biggeri A, Böhning D, Lessafre E, Viel J, Bertollini R, eds. Disease mapping and risk assessment for public health. Wiley, New York ; 1999.
23. Banerjee S., Carlin BP, Gelfand AE Hierarchical modeling and analysis for spatial data. Chapman & Hall/CRC, Boca Raton, FL ; 2004.
24. Reich BJ Neighbor relation modelling and variance component identification in hierarchical areal data models with application to periodontology, cancer epidemiology, and sports. PhD dissertation, University of Minnesota, Minneapolis, MN ; 2005.
25. Reich BJ, Bandyopadhyay D. A latent factor model for spatial data with informative missingness. Annals of Applied Statistics 2010 ; 4 (1). 439-59.
26. Spiegelhalter DJ, Best NG, Carlin BP, van der Linde A. Bayesian measures of model complexity and fit (with discussion). Journal of the Royal Statistical Society Ser. B 2002 ; 64: 583-639.
27. Gelfand AE, Dey DK Bayesian model choice: asymptotics and exact calculations. Journal of the Royal Statistical Society, Series B 1994 ; 56: 501-14.
28. Darby ML, Walsh MM Dental hygiene: theory and practice (1st edn). W. B. Saunders Company, USA; 1995.
29. Broadbent JM, Thompson WM For debate: problems with the DMF index pertinent to dental caries data analysis. Community dentistry and Oral Epidemiology 2005 ; 33 (6). 400-9. (Pubitemid 43906607)
30. Johnson-Spruill I., Hammond P., Davis B., McGee Z., Louden D. Health of Gullah families in South Carolina with Type-2 diabetes, The Diabetes Educator 2009 ; 35: 117-23.
31. Abramowitz M., Stegun IA Handbook of Mathematical Functions. Dover, New York ; 1965.
32. Skellam JG A probability distribution from the binomial distribution by regarding the probability of success as variable between the sets of trials. Journal of the Royal Statistical Society, Ser. B 1948 ; 10: 257-65.
33. MacEachern S., Kottas A., Gelfand A. Spatial nonparametric Bayesian models. Technical Report 01-10, Institute of Statistics and Decision Sciences, Duke University, 2001.
34. Jiang J. Linear and generalized linear mixed models and their applications. Springer-Verlag, New York ; 2007.
35. Besag J., York JC, Mollié A. Bayesian image restoration, with two applications in spatial statistics (with discussions). Annals of the Institute of Statistical Mathematics 1991 ; 43: 1-59.
36. Cressie NAC. Statistics for spatial data (revised edn). Wiley, New York ; 1993.
37. Carlin BP, Banerjee S. Hierarchical multivariate CAR models for spatio-temporally correlated survival data (with discussion). In Bernardo JM, Bayarri MJ, Berger JO, Dawid AP, Heckerman D, Smith AFM, West M, eds. Bayesian statistics 7. Oxford University Press, Oxford ; 2003: 45-63.
38. McCullagh P., Nelder J. Generalized Linear Models (2 nd edn). Chapman and Hall/CRC, New York ; 1989.
39. Spiegelhalter D., Thomas A., Best N., Lunn D. WinBUGS User Manual, Version 1.4.2, MRC Biostatistics Unit, Institute of Public Health and Department of Epidemiology and Public Health, Imperial College School of Medicine. Available at: http://www.mrc-bsu.cam.ac.uk/bugs, 2005 (accessed November-December 2009 ).
40. Dunson DB, Chen Z., Harry J. A Bayesian approach for joint modeling of cluster size and subunit-specific outcomes. Biometrics 2003 ; 59: 521-30. (Pubitemid 37093391)
41. Best NG, Arnold RA, Thomas A., Waller LA, Conlon EM Bayesian models for spatially correlated disease and exposure data (with discussion). In Bernardo JM, Berger JO, Dawid AP, Smith AFM, eds. Bayesian statistics 6. Oxford University Press, Oxford ; 2003: 131-56.
42. Gelfand AE, Sahu SK, Carlin BP Efficient parameterisations for generalised linear models (with discussion). In Bernardo JM, Berger JO, Dawid AP, Smith AFM, eds. Bayesian statistics 5. Oxford University Press, Oxford ; 2003: 165-80.
43. Gelman A., Carlin JB, Stern H., Rubin D. Bayesian data analysis (2nd edn). Chapman & Hall / CRC, Florida ; 2004.
44. Daniels MJ, Kass RE Nonconjugate Bayesian estimation of covariance matrices and its use in hierarchical models. Journal of the American Statistical Association 1999 ; 94: 1254-63.
45. Zhou H., Lawson AB, Hebert JR, Slate EH, Hill EG A Bayesian hierarchical modeling approach for studying the factors affecting the stage at diagnosis of prostate cancer. Statistics in Medicine 2008 ; 27: 3612-28.