Spline smoothing in Bayesian disease mapping

Environmetrics

Volumn 18, Issue 7, 2007, Pages 727-744

  MacNab, Ying C ^a,b  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Bayesian disease mapping; Multivariate conditional autoregressive (MCAR) prior; P spline; Regression spline; Smoothing spline; Spatiotemporal models

Indexed keywords

BAYESIAN ANALYSIS; CHILD HEALTH; DISEASE; HOSPITAL SECTOR; MAPPING METHOD; MARKOV CHAIN; MODELING; MONTE CARLO ANALYSIS;

BRITISH COLUMBIA; CANADA; NORTH AMERICA;

EID: 35348948366     PISSN: 11804009     EISSN: 1099095X     Source Type: Journal    
DOI: 10.1002/env.876     Document Type: Conference Paper

References (34)

1. Böhning D, Dietz E, Schlattmann P. 2000. Space-time mixture modeling of public health data. Statistics in Medicine 17/18: 2333-2344.
2. Breslow NE, Clayton DG. 1993. Approximate inference in generalized linear mixed models. Journal of the American Statistical Association 88: 9-25.
3. Brezger A,d Lang S. 2006. Generalized structured additive regression based on Bayesian P-splines. Computational statistics & Data Analysis 50: 967-991.
4. Brumback BA, Rice JA. 1998. Smoothing spline models for the analysis of nested and crossed samples of curves (with discussion). Journal of the American Statistical Association 93(443): 961-994.
5. Durban M, Harezlak J, Wand MP, Carroll RJ. 2004. Simple fitting of subject-specific curves for longitudinal data. Statistics in Medicine 24: 1-24.
6. Eilers PHC, Marx BD. 1996. Flexible smoothing using B-splines with penalized likelihood (with comments ad rejoinder). Statistical Science 11(2): 89-121.
7. Friedman JH, Silverman BW. 1989. Flexible parsimonious smoothings and additive modeling. Technometrics 31: 3-39.
8. Fahrmeir L, Kneib T, Lang S. 2004. Penalized structured additive regressive for space-time data: a Bayesian perspective. Statistica Sinica 14: 731-761.
9. Green PJ, Silverman BW. 2000. Nonparametric Regression and Generalize Linear Models. Chapman & Hall/CRC: New York.
10. Hastie TJ, Tibshirani RJ. 1990. Generalized Additive Models. Chapman & Hall/CRC: New York.
11. Hastie TJ, Tibshirani RJ. 2000. Bayesian backfitting. Statistical Science 15: 193-223.
12. Knorr-Held L, Richardson S. 2003. A hierarchical model for space-time surveillance data on meningococcal disease incidence. Applied Statistics 52: 169-183.
13. Lambert P, Eilers PH. 2005. Bayesian proportional hazards model with time-varying regression coefficients: a penalized Poisson regression approach. Statistics in Medicine 24: 3977-3989.
14. Lang S, Brezger A. 2004. Bayesian P-splines. Journal of Computational and Graphic Statistics 13: 183-212.
15. Lawson A, Biggeri A, Böhning D, Lesaffre E, Viel J-F, Bertollini R (eds). 1999. Disease Mapping and Risk Assessment for Public Health. John Wiley & Sons: New York.
16. Leroux BG, Lei X, Breslow N. 1999. Estimation of disease rates in small areas: a new mixed model for spatial dependence. In Statistical Models in Epidemiology, the Environment and Clinical Trials, Halloran ME, Berry D (eds). Springer-Verlag: New York; 135-178.
17. Lin X, Zhang D. 1999. Inference in generalized additive mixed models by using smoothing splines. Journal of the Royal Statistical Society 61B: 381-400.
18. MacNab YC, Dean BC. 2001. Autoregressive spatial smoothing and temporal smoothing B-splines for mapping rates. Biometrics 57(3): 949-956.
19. MacNab YC, Kmetic A, Gustafson P, Snaps S. 2006. An innovative application of Bayesian disease mapping methods to patient safety research: the Canadian iatrogenic injury study. Statistics in Medicine 35(23): 3960-3980.
20. MacNab YC, Gustafson P. 2007. Regression B-spline smoothing in Bayesian disease mapping: with an application to patient safety surveillance. Statistics in Medicine, DOI: 10.1002/sim.2868.
21. MacNab YC. 2007. Mapping disability-adjusted life year (DALY): a Bayesian DALY methodology for regional study of disease and injury burden. Statistics in Medicine, DOI: 10.1002/sim.2890.
22. O'Sullivan F. 1986. A statistical perspective on ill-posed inverse problems (with discussion). Statistical Science 1: 505-527.
23. Ruppert D. 2002. Selecting the number of knots for penalized splines. Journal of Computational and Graphical Statistics 11: 735-757.
24. Ruppert D, Carroll RJ. 2000. Spatially-adaptive penalties for spline fitting. Australian and New Zealand Journal of Statistics 42: 205-223.
25. Ruppert D, Wand MP, Carroll RJ. 2003. Semiparametric Regression. University Press: Cambridge.
26. Silverman BW. 1985. Some aspects of the spline smoothing approach to non-parametric regression curve fitting (with discussion). Journal of the Royal Statistical Society B(47): 1-52.
27. Spiegelhalter DJ, Best NG, Carlin BP, van der Linde A. 2003a. Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society Series B 64: 583-639.
28. Spiegelhalter DJ, Thomas A, Best N, Lunn D. 2003b. WinBUGS version 1.4 user manual. MRC Biostatistics Unit, Institute of Public Health, Cambridge University: Cambridge.
29. Ugarte MD, Ibez B, Militino AF. 2006. Modelling Risks in Disease Mapping. Statistical Methods in Medical Research 15: 21-35.
30. Verbyla AP, Cullis BR, Kenward MG, Welham SJ. 1999. The analysis of designed experiments and longitudinal data by using smoothing splines (with discussion). Applied Statistics 48(3): 269-311.
31. Waller LA, Carlin BP, Xia H, Gelfand AE. 1997. Hierarchical spatio-temporal mapping of disease rates, Journal of the American Statistical Association 92: 607-617.
32. Wand M. 2000. A comparison of regression spline smoothing procedures. Computational Statistics 15: 443-462.
33. White IMS, Thompson R, Brotherstone S. 1999. Genetic and environmental smoothing of lactation curves with cubic splines. Journal of Diary Science 82: 632-638.
34. Zhao Y, Staudenmayer J, Coull BA, Wand MP. 2006. General design Bayesian generalized linear mixed models. Statistical Science 21(1): 35-51.