Estimating the functional form of a continuous covariate's effect on survival time

Computational Statistics and Data Analysis

Volumn 50, Issue 4, 2006, Pages 1131-1151

  Holländer, Norbert ^a   Schumacher, Martin ^a  

^a UNIVERSITY OF FREIBURG   (Germany)

Author keywords

Bootstrap aggregating; Model building; Proportional hazards model; Risk function

Indexed keywords

DATA REDUCTION; PARAMETER ESTIMATION; POLYNOMIALS; RISKS; TUMORS;

BREAST CANCER; CATEGORIZATION; DATA-DRIVEN RISK FUNCTIONS; FRACTIONAL POLYNOMIALS;

MATHEMATICAL MODELS;

EID: 26444590486     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2004.11.008     Document Type: Article

References (43)

1. M. Abrahamowicz, T. MacKenzie, and J. Esdaile Time-dependent hazard ratio modeling and hypothesis testing with application in lupus nephritis J. Amer. Statist. Assoc. 91 1996 1432 1439
2. M. Abrahamowicz, T. Schopflocher, K. Leffondré, R. du Berger, and D. Krewski Flexible modeling of exposure-response relationship between long-term average levels of particulate air pollution and mortality in the American Cancer Society Study J. Toxicol. Environ. Health, Part A 66 2003 1625 1653
3. D. Altman, B. Lausen, W. Sauerbrei, and M. Schumacher Dangers of using "optimal" cutpoints in the evaluation of prognostic factors. Commentary J. Nat. Cancer Inst. 86 1994 829 835
4. G. Ambler, and P. Royston Fractional polynomial model selection procedures investigation of type I error rate J. Statist. Comput. Simul. 69 2001 89 108
5. P. Andersen, O. Borgan, R. Gill, and N. Keiding Statistical Methods Based on Counting Processes 1993 Springer New York
6. L. Breiman Bagging predictors Mach. Learning 26 1996 123 140
7. L. Breiman, J.H. Friedman, R.J. Olsen, and C.J. Stone Classification and Regression Trees 1984 Wadsworth Monterey
8. P. Bühlmann, and B. Yu Analyzing bagging Ann. Statist. 30 2002 927 961
9. C. Contal, and J. O'Quigley An application of changepoint methods in studying the effect of age on survival in breast cancer Comput. Statist. Data Anal. 30 1999 253 270
10. D.R. Cox Regression models and life tables (with discussion) J. Roy. Statist. Soc., Ser. B 34 1972 187 220
11. A. Davison, and D. Hinkley Bootstrap Methods and their Applications 1997 Cambridge University Press New York
12. A. De la Rochefordiere, B. Asselain, F. Campana, S. Scholl, J. Fenton, J. Viloq, J.-C. Durand, P. Pouillart, H. Magdelenat, and A. Fourquet Age as prognostic factor in premenopausal breast carcinoma Lancet 341 1993 1039 1043
13. B. Efron, and R. Tibshirani An Introduction to the Bootstrap 1993 Chapman & Hall New York
14. A. Ezzat, M. Raja, F. Zwaan, M. Brigden, A. Rostom, and S. Bazarbashi The lack of age as a significant prognostic factor in non-metastatic breast cancer Eur. J. Surg. Oncol. 1 1998 23 27
15. E. Fisher, S. Anderson, E. Tan-Chiu, B. Fisher, L. Eaton, and N. Wolmark Fifteen-year prognostic discriminants for invasive breast carcinoma Cancer (Suppl) 91 2001 1679 1687
16. E. Graf, C. Schmoor, W. Sauerbrei, and M. Schumacher Assessment and comparison of prognostic classification schemes for survival data Statist. Med. 18 1999 2529 2545
17. R. Gray Flexible methods for analyzing survival data using splines, with applications to breast cancer prognosis J. Amer. Statist. Assoc. 87 1992 942 951
18. F.E. Harrell Regression Modeling Strategies with Applications to Linear Models, Logistic Regression and Survival Analysis 2001 Springer New York
19. R. Hashemi, and D. Commenges Correction of the p-value after multiple tests in a Cox proportional hazard model Lifetime Data Anal. 8 2002 335 348
20. Holländer, N., 2002. Estimating the functional form of the effect of a continuous covariate on survival time. Dortmund, Ph.D. Thesis, University of Dortmund.
21. N. Holländer, and M. Schumacher On the problem of using 'optimal' cutpoints in the assessment of quantitative prognostic factors Onkologie 24 2001 194 199
22. T. Hothorn, and B. Lausen On the exact distribution of maximally selected rank statistics Comput. Statist. Data Anal. 43 2003 121 137
23. T. Hothorn, B. Lausen, A. Benner, and M. Radespiel-Tröger Bagging survival trees Statist. Med. 23 2004 77 91
24. J. Kalbfleisch, and R. Prentice The Statistical Analysis of Failure Time Data 1980 Wiley New York
25. J. Klein, and J.-T. Wu Discretizing a continuous covariate in survival studies N. Balakrishnan C. Rao Handbook of Statistics vol. 23 2004 Elsevier Amsterdam 27 42
26. N. Kroman, M.-B. Jensen, J. Wohlfahrt, H. Mouridsen, P. Andersen, and M. Melbye Factors influencing the effect of age on prognosis in breast cancer Population study Br. Med. J. 320 2000 474 479
27. B. Lausen, and M. Schumacher Maximally selected rank statistics Biometrics 48 1992 73 85
28. B. Lausen, and M. Schumacher Evaluating the effect of optimized cutoff values in the assessment of prognostic factors Comput. Statist. Data Anal. 21 1996 307 326
29. E. Marubini, and M.G. Valsecchi Analysing Survival Data from Clinical Trials and Observational Studies 1995 Wiley New York
30. P. Royston, and D. Altman Regression using fractional polynomials of continuous covariates parsimonious parametric modelling (with discussion) Appl. Statist. 43 1994 429 467
31. P. Royston, and W. Sauerbrei Stability of multivariable fractional polynomial models with selection of variables and transformations a bootstrap investigation Statist. Med. 22 2003 639 659
32. W. Sauerbrei, and P. Royston Building multivariable prognostic and diagnostic models transformation of the predictors by using fractional polynomials J. Roy. Statist. Soc. Ser. A 162 1999 71 94
33. W. Sauerbrei, P. Royston, H. Bojar, C. Schmoor, and M. Schumacher Modelling the effects of standard prognostic factors in node-positive breast cancer Br. J. Cancer 79 1999 1752 1760
34. M. Schumacher, G. Bastert, H. Bojar, K. Hübner, M. Olschewski, W. Sauerbrei, C. Schmoor, C. Beyerle, R. Neumann, and H. Rauschecker Randomized 2 × 2 trial evaluating hormonal treatment and the duration of chemotherapy in node-positive breast cancer patients J. Clin. Oncol. 12 1994 2086 2093
35. M. Schumacher, N. Holländer, and W. Sauerbrei Resampling and cross-validation techniques a tool to reduce bias caused by model building Statist. Med. 16 1997 2813 2827
36. M. Schumacher, N. Holländer, G. Schwarzer, and W. Sauerbrei Prognostic factor studies J. Crowley Handbook of Statistical Methods in Clinical Oncology 2001 Dekker New York 321 378
37. L. Sleeper, and D. Harrington Regression splines in the Cox model with application to covariate effects in liver disease J. Amer. Statist. Assoc. 85 1990 941 949
38. StataCorp, 2001. Stata statistical software: release 7.0. Stata Corporation, Texas: College Station.
39. Statistical Sciences, 1993. S-PLUS programmer's manual, Version 3.2. Seattle: Statistical Sciences, a division of MathSoft Inc.
40. T.M. Therneau, P.M. Grambsch, and T.R. Fleming Martingale based residuals for survival models Biometrika 48 1990 147 160
41. R. Tibshirani, and T. Hastie Local likelihood estimation J. Amer. Statist. Assoc. 82 1987 559 567
42. H. Van Houwelingen, and S. Le Cessie Predictive value of statistical models Statist. Med. 9 1990 1303 1325
43. P. Verweij, and H. Van Houwelingen Time-varying covariates of fixed covariates in Cox regression Biometrics 51 1995 1550 1556