Table of Contents Author Guidelines Submit a Manuscript
Journal of Probability and Statistics
Volume 2009, Article ID 198320, 24 pages
http://dx.doi.org/10.1155/2009/198320
Research Article

Investigating Determinants of Multiple Sclerosis in Longitunal Studies: A Bayesian Approach

1University Centre of Statistics in the Biomedical Sciences, (CUSSB), Vita-Salute University, Milan, Italy
2Division of Genetic Epidemiology, Department of Medical Genetics, Molecular and Clinical Pharmacology, Innsbruck Medical University, Innsbruck, Austria

Received 3 September 2008; Revised 3 February 2009; Accepted 12 August 2009

Academic Editor: Kelvin K. W. Yau

Copyright © 2009 Clelia Di Serio and Claudia Lamina. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. H. Noseworthy, M. K. Vandervoort, C. J. Wong, and G. C. Ebers, “Interrater variability with the expanded disability status scale (EDSS) and functional systems (FS) in a multiple sclerosis clinical trial,” Neurology, vol. 40, no. 6, pp. 971–975, 1990. View at Google Scholar
  2. M. Soilu-Hänninen, J. O. Koskinen, M. Laaksonen, A. Hänninen, E.-M. Lilius, and M. Waris, “High sensitivity measurement of CRP and disease progression in multiple sclerosis,” Neurology, vol. 65, no. 1, pp. 153–155, 2005. View at Publisher · View at Google Scholar · View at PubMed
  3. S. Esbjerg, N. Keiding, and N. Koch-Henriksen, “Reporting delay and corrected incidence of multiple sclerosis,” Statistics in Medicine, vol. 18, no. 13, pp. 1691–1706, 1999. View at Google Scholar
  4. P. S. Albert, H. F. McFarland, M. E. Smith, and J. A. Frank, “Repeated measures time series for modelling counts from a relapsing-remitting disease: application to modelling disease activity in multiple sclerosis,” Statistics in Medicine, vol. 13, pp. 453–466, 1994. View at Publisher · View at Google Scholar
  5. W. I. McDonald, A. Compston, G. Edan et al., “Recommended diagnostic criteria for multiple sclerosis: guidelines from the international panel on the diagnosis of multiple sclerosis,” Annals of Neurology, vol. 50, no. 1, pp. 121–127, 2001. View at Publisher · View at Google Scholar
  6. T. Hastie and R. Tibshirani, “Bayesian backfitting,” Statistical Science, vol. 15, no. 3, pp. 196–223, 2000. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. L. Fahrmeir and S. Lang, “Bayesian inference for generalized additive mixed models based on Markov random field priors,” Journal of the Royal Statistical Society C, vol. 50, no. 2, pp. 201–220, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  8. L. Fahrmeir and S. Lang, “Bayesian semiparametric regression analysis of multicategorical time-space data,” Annals of the Institute of Statistical Mathematics, vol. 53, no. 1, pp. 11–30, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. T. Kneib and L. Fahrmeir, “Structured additive regression for categorical space-time data: a mixed model approach,” Biometrics, vol. 62, no. 1, pp. 109–118, 2006. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. M. J. Lindstrom and D. M. Bates, “Nonlinear mixed effects models for repeated measures data,” Biometrics, vol. 46, no. 3, pp. 673–687, 1990. View at Google Scholar · View at MathSciNet
  11. E. F. Vonesh and V. M. Chinchilli, Linear and Nonlinear Models for the Analysis of Repeated Measurements, vol. 154 of Statistics: Textbooks and Monographs, Marcel Dekker, New York, NY, USA, 1997. View at MathSciNet
  12. G. Verbeke and G. Molenberghs, Linear Mixed Models for Longitudinal Data, Springer Series in Statistics, Springer, New York, NY, USA, 2000. View at MathSciNet
  13. P. J. Diggle, P. J. Heagerty, K.-Y. Liang, and S. L. Zeger, Analysis of Longitudinal Data, vol. 25 of Oxford Statistical Science Series, Oxford University Press, Oxford, UK, 2nd edition, 2002. View at MathSciNet
  14. T. J. Hastie and R. J. Tibshirani, Generalized Additive Models, vol. 43 of Monographs on Statistics and Applied Probability, Chapman & Hall/CRC, London, UK, 1990. View at MathSciNet
  15. S. Lang and A. Brezger, “Bayesian P-splines,” Journal of Computational and Graphical Statistics, vol. 13, no. 1, pp. 183–212, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  16. J. F. Kurtzke, “Rating neurologic impairment in multiple sclerosis: an expanded disability status scale (EDSS),” Neurology, vol. 33, pp. 1444–1452, 1983. View at Google Scholar
  17. R. Bergamaschi, A. Romani, S. Tonietti, A. Citterio, C. Berzuini, and V. Cosi, “Usefulness of Bayesian graphical models for early prediction of disease progression in multiple sclerosis,” Neurological Sciences, vol. 21, no. 8, pp. S819–S823, 2000. View at Publisher · View at Google Scholar
  18. L. Fahrmeir and G. Tutz, Multivariate Statistical Modelling Based on Generalized Linear Models, Springer Series in Statistics, Springer, New York, NY, USA, 2nd edition, 2001. View at MathSciNet
  19. C. Ke and Y. Wang, “Semiparametric nonlinear mixed-effects models and their applications,” Journal of the American Statistical Association, vol. 96, no. 456, pp. 1272–1298, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. J. J. Faraway, Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models, Texts in Statistical Science Series, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2006. View at MathSciNet
  21. S. R. Searle, G. Casella, and C. E. McCulloch, Variance Components, John Wiley & Sons, New York, NY, USA, 1992. View at MathSciNet
  22. B. D. Marx and P. H. C. Eilers, “Direct generalized additive modeling with penalized likelihood,” Computational Statistics and Data Analysis, vol. 28, no. 2, pp. 193–209, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  23. P. H. C. Eilers and B. D. Marx, “Flexible smoothing with B-splines and penalties,” Statistical Science, vol. 11, no. 2, pp. 89–121, 1996. View at Google Scholar · View at MathSciNet
  24. A. Brezger and S. Lang, “Generalized structured additive regression based on Bayesian P-splines,” Computational Statistics & Data Analysis, vol. 50, no. 4, pp. 967–991, 2006. View at Google Scholar · View at MathSciNet
  25. G. Kauermann, T. Krivobokova, and F. Ludwig, “Some asymptotic results on generalized penalized spline smoothing,” Tech. Rep., Department of Decision Sciences and Information Management (KBI), Katholieke Universiteit, Leuven, Belgium, 2007. View at Google Scholar
  26. W. Gilks, S. Richardson, and D. Spiegelhalter, Markov Chain Monte Carlo in Practice, Interdisciplinary Statistics, Chapman & Hall/CRC, Boca Raton, Fla, USA, 1996. View at MathSciNet
  27. G. Tutz, Die Analyse Kategorialer Daten, Oldenbourg Wissenschaftesverlag, Munich, Germany, 2000.
  28. A. Brezger, T. Kneib, and S. Lang, “BayesX: analysing Bayesian structured additive regression models,” Journal of Statistical Software, vol. 14, p. 11, 2005. View at Google Scholar
  29. D. Hedeker and R. D. Gibbons, “A random-effects ordinal regression model for multilevel analysis,” Biometrics, vol. 50, no. 4, pp. 933–944, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH