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Applications and Case Studies

Regression Splines in the Cox Model with Application to Covariate Effects in Liver Disease

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Pages 941-949 | Received 01 May 1989, Published online: 27 Feb 2012

References

  • Akaike , H. Information Theory and an Extension of the Maximum Likelihood Principle . 2nd International Symposium on Information Theory . Edited by: Petrov , B. N. and Czáki , F. Budapest : Akademiai Kiadó .
  • Barlow , W. E. and Prentice , R. L. 1988 . Residuals for Relative Risk Regression . Biometrika , 75 : 65 – 74 .
  • Cox , D. R. 1972 . Regression Models and Life-Tables . Journal of the Royal Statistical Society , 34 : 187 – 220 . (with discussion), Ser. B
  • Curry , H. B. and Schoenberg , I. J. 1966 . On Polya Frequency Functions. IV: The Fundamental Spline Functions and Their Limits . Journale d'Analyse Mathématique , 17 : 71 – 107 .
  • de Boor , C. 1978 . A Practical Guide to Splines , New York : Springer .
  • Devlin , T. F. and Weeks , B. J. Spline Functions for Logistic Regression Modeling . Proceedings of the SAS Users’ Group International Conference . pp. 646 – 649 . Cary , NC : SAS Institute Inc .
  • Dickson , E. R. , Grambsch , P. , Fleming , T. R. , Fisher , L. D. and Langworthy , A. 1989 . Prognosis in Primary Biliary Cirrhosis: Model for Decision Making . Hepatology , 10 : 1 – 7 .
  • Durrleman , S. and Simon , R. 1989 . Flexible Regression Models With Cubic Splines . Statistics in Medicine , 8 : 551 – 561 .
  • Friedman , J. H. and Silverman , B. W. 1989 . Flexible Parsimonious Smoothing and Additive Modeling (with discussion) . Technometrics , 31 : 3 – 39 .
  • Harrell , F. E. , Lee , K. L. and Pollock , B. G. 1988 . Regression Models in Clinical Studies: Determining Relationships Between Predictors and Response . Journal of the National Cancer Institute , 80 : 1198 – 1202 .
  • Hastie , T. and Tibshirani , R. 1986 . Generalized Additive Models . Statistical Science , 1 : 297 – 318 . (with discussion)
  • Jupp , D. L. B. 1978 . Approximation of Data by Splines With Free Knots . SIAM Journal on Numerical Analysis , 15 : 328 – 343 .
  • Kuk , A. Y. 1984 . All Subsets Regression in a Proportional Hazards Model . Biometrika , 71 : 587 – 592 .
  • Moolgavkar , S. H. and Venzon , D. J. 1986 . “ Confidence Regions for Case-Control and Survival Studies With General Relative Risk Functions ” . In Modern Statistical Methods in Chronic Disease Epidemiology , Edited by: Moolgavkar , S. H. and Prentice , R. L. New York : John Wiley .
  • O'Sullivan , F. 1988 . Nonparametric Estimation of Relative Risk Using Splines and Cross-Validation . SIAM Journal on Scientific and Statistical Computing , 9 : 531 – 542 .
  • Peto , R. 1972 . Contribution to the Discussion of Paper by D. R. Cox . Journal of the Royal Statistical Society , 34 : 205 – 207 . Ser. B
  • Smith , P. L. 1979 . Splines as a Useful and Convenient Statistical Tool . The American Statistician , 33 : 57 – 62 .
  • Smith , P. L. 1982 . Hypothesis Testing in B-Spline Regression . Communications in Statistics B–Simulation and Computation , 11 : 143 – 157 .
  • Stone , C. J. 1985 . Additive Regression and Other Nonparametric Models . The Annals of Statistics , 13 : 689 – 705 .
  • Stone , C. J. and Koo , C.-Y. Additive Splines in Statistics . Proceedings of the Statistical Computing Section . pp. 45 – 48 . American Statistical Association .
  • Stone , M. 1977 . An Asymptotic Equivalence of Choice of Model by Cross-Validation and Akaike's Criterion . Journal of the Royal Statistical Society , 39 : 44 – 47 . Ser. B
  • Therneau , T. , Grambsch , P. and Fleming , T. R. 1990 . Martingale Based Residuals for Survival Models . Biometrika , 77 : 147 – 160 .
  • Tibshirani , R. and Hastie , T. 1987 . Local Likelihood Estimation . Journal of the American Statistical Association , 82 : 559 – 567 .
  • Wold , S. 1974 . Spline Functions in Data Analysis . Technometrics , 16 : 1 – 11 .

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