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Computational and Mathematical Methods in Medicine
Volume 2012 (2012), Article ID 986176, 9 pages
http://dx.doi.org/10.1155/2012/986176
Research Article

Survival Data Analysis with Time-Dependent Covariates Using Generalized Additive Models

1Department of Engineering Informatics, Osaka Electro-Communication University, Osaka 572-8530, Japan
2Clinical Information Division, Data Science Center, EPS Corporation, Osaka 532-0003, Japan
3Nishinomiya Municipal Central Hospital, Hyogo 663-8014, Japan

Received 16 July 2011; Accepted 11 January 2012

Academic Editor: Hugo Palmans

Copyright © 2012 Masaaki Tsujitani et al. 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. E. R. Dickson, P. M. Grambsch, T. R. Fleming, L. D. Fisher, and A. Langworthy, “Prognosis in primary biliary cirrhosis: model for decision making,” Hepatology, vol. 10, no. 1, pp. 1–7, 1989. View at Scopus
  2. D. R. Cox, “Regression models and life tables (with discussion),” Journal of the Royal Statistical Society: Series B, vol. 34, pp. 187–220, 1972.
  3. D. G. Altman and B. L. de Stavola, “Practical problems in fitting a proportional hazards model to data with updated measurements of the covariates,” Statistics in Medicine, vol. 13, no. 4, pp. 301–341, 1994. View at Scopus
  4. D. Collett, Modelling Survival Data in Medical Research, Chapman & Hall/CRC, London, UK, 2nd edition, 2003.
  5. J. P. Klein and M. L. Moeschberger, Survival Analysis, Springer, New York, NY, USA, 2nd edition, 2003.
  6. J. F. Lawless, Statistical Models and Methods for Lifetime Data, John Wiley, New York, NY, USA, 2nd edition, 2003.
  7. P. A. Murtaugh, E. R. Dickson, G. M. van Dam et al., “Primary biliary cirrhosis: prediction of short-term survival based on repeated patient visits,” Hapatology, vol. 20, pp. 126–134, 1994.
  8. T. M. Therneau and P. M. Grambsch, Modeling Survival Data: Extending the Cox Model, Springer, New York, NY, USA, 2000.
  9. J. D. Kalbfleisch and R. L. Prentice, The Statistical Analysis of Failure Time Data, John Wiley, New York, NY, USA, 2nd edition, 2002.
  10. E. Marubini and M. G. Valsecchi, Analysing Survival Data from Clinical Trials and Observational Studies, John Wiley, New York, NY, USA, 1995.
  11. E. Christensen, P. Schlichting, P. K. Andersen et al., “Updating prognosis and therapeutic effect evaluation in cirrhosis with Cox’s multiple regression model for time-dependent variables,” Scandinavian Journal of Gastroenterology, vol. 21, no. 163, pp. 174–1986.
  12. E. Christensen, D. G. Altman, J. Neuberger et al., “Updating prognosis in primary biliary cirrhosis using a timedependent Cox regression model,” Gastroenterology, vol. 105, pp. 1865–1876, 1993.
  13. T. J. Hastie and R. J. Tibshirani, Generalized Additive Models, Chapman & Hall, London, NY, USA, 1990.
  14. L. A. Sleeper and D. P. Harrington, “Regression splines in the Cox model with application to covariate effects in liver disease,” Journal of the American Statistical Association, vol. 85, pp. 941–949, 1990.
  15. R. J. Gray, “Flexible methods for analyzing survival data using splines,with applications to breast cancer prognosis,” Journal of the American Statistical Association, vol. 87, pp. 942–951, 1992.
  16. R. Giorgi and J. Gouvernet, “Analysis of time-dependent covariates in a regressive relative survival model,” Statistics in Medicine, vol. 24, no. 24, pp. 3863–3870, 2005. View at Publisher · View at Google Scholar · View at PubMed · View at MathSciNet · View at Scopus
  17. J. Ding and J. L. Wang, “Modeling longitudinal data with nonparametric multiplicative random effects jointly with survival data,” Biometrics, vol. 64, no. 2, pp. 546–556, 2008. View at Publisher · View at Google Scholar · View at PubMed · View at Scopus
  18. R. Schoop, E. Graf, and M. Schumacher, “Quantifying the predictive performance of prognostic models for censored survival data with timedependent covariates,” Biometrics, vol. 64, pp. 603–610, 2008.
  19. E. Arjas, “A graphical method for assessing goodness of fit in Cox’s proportional hazards model,” Journal of the American Statistical Association, vol. 83, pp. 204–212, 1988.
  20. E. Biganzoli, P. Boracchi, L. Mariani, and E. Marubini, “Feed forward neural networks for the analysis of censored survival data: a partial logistic regression approach,” Statistics in Medicine, vol. 17, no. 10, pp. 1169–1186, 1998. View at Publisher · View at Google Scholar · View at Scopus
  21. E. Biganzoli, P. Boracchi, and E. Marubini, “A general framework for neural network models on censored survival data,” Neural Networks, vol. 15, no. 2, pp. 209–218, 2002. View at Publisher · View at Google Scholar · View at Scopus
  22. D. R. Cox, “Partial likelihood,” Biometrika, vol. 62, no. 2, pp. 269–276, 1975. View at Scopus
  23. B. Efron, “Logistic regression, survival analysis, and Kaplan-Meier curve,” Journal of the American Statistical Association, vol. 83, pp. 414–425, 1988.
  24. M. Tsujitani and M. Sakon, “Analysis of survival data having time-dependent covariates,” IEEE Transactions on Neural Networks, vol. 20, no. 3, pp. 389–394, 2009. View at Publisher · View at Google Scholar · View at PubMed · View at Scopus
  25. P. McCullagh and J. A. Nelder, Generalized Linear Models, Chapman & Hall, London, UK, 2nd edition, 1989.
  26. P. K. Andelsen and R. D. Gill, “Cox’s regression model for counting process: a large sample study,” Annals of Statistics, vol. 10, pp. 1100–1120, 1982.
  27. S. N. Wood, Generalized Additive Models: An Introduction with R, Chapman & Hall, London, UK, 2006.
  28. S. N. Wood, “Stable and efficient multiple smoothing parameter estimation for generalized additive models,” Journal of the American Statistical Association, vol. 99, pp. 673–686, 2004.
  29. S. N. Wood, “Fast stable direct fitting and smoothness selection for generalized additive models,” Journal of the Royal Statistical Society: Series B, vol. 70, no. 3, pp. 495–518, 2008. View at Publisher · View at Google Scholar · View at Scopus
  30. P. Zhang, “Model selection via multifold cross validation,” Annals of Statistics, vol. 21, pp. 299–313, 1993.
  31. J. M Landwehr, D. Pregibon, and A. C. Shoemaker, “Graphical methods for assessing logistic regression models,” Journal of the American Statistical Association, vol. 79, pp. 61–71, 1984.
  32. M. Tsujitani and T. Koshimizu, “Neural discriminant analysis,” IEEE Transactions on Neural Networks, vol. 11, no. 6, pp. 1394–1401, 2000. View at Scopus
  33. D. Collett, Modelling Binary Data, Chapman & Hall/CRC, London, UK, 2nd edition, 2003.
  34. B. Efron and R. J. Tibshirani, An Introduction to the Bootstrap, Chapman & Hall, London, UK, 1993.
  35. B. H. Markus, E. R. Dickson, P. M. Grambsch et al., “Efficacy of liver transplantation in patients with primary biliary cirrhosis,” The New England Journal of Medicine, vol. 320, no. 26, pp. 1709–1713, 1989. View at Scopus
  36. B. L. Thomsen, N. Keiding, and D. G. Altman, “A note on the calculation of expected survival, illustrated by the survival of liver transplant patients,” Statistics in Medicine, vol. 10, no. 5, pp. 733–738, 1991. View at Scopus
  37. J. Crowley and M. Hu, “Covariance analysis of heart transplant survival data,” Journal of the American Statistical Association, vol. 72, pp. 27–36, 1977.
  38. M. Pintilie, Competing Risks: A Practical Perspective, John Wiley, New York, NY, USA, 2006.
  39. T. J. Hastie, R. J. Tibshirani, and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Springer, New York, NY, USA, 2001.
  40. C. Gu, “Smoothing Spline ANOVA Models,” pp. Springer–New York, NY, USA, 2002.
  41. E. T. Lee and J. W. Wang, Statistical Methods for Survival Data Analysis, John Wiley, New York, NY, USA, 3rd edition, 2003.
  42. L. J. Wei, D. Y. Lin, and L. Wessfeld, “Regression analysis of multivariate incomplete failure time data by modeling marginal distributions,” Journal of the American Statistical Association, vol. 84, pp. 1065–1073, 1989.