155
Views
9
CrossRef citations to date
0
Altmetric
Inference

Selecting the Optimal Transformation of a Continuous Covariate in Cox's Regression: Implications for Hypothesis Testing

, , &
Pages 27-45 | Received 07 Mar 2003, Accepted 05 May 2005, Published online: 15 Feb 2007

References

  • Abrahamowicz , M. , Mackenzie , T. , Esdaile , J. K. ( 1996 ). Time dependent hazard ratio: modeling and hypothesis testing with application in lupus nephritis . J. Amer. Statist. Assoc. 44 : 214 – 217 . [CSA]
  • Abrahamowicz , M. , Du Berger , R. , Grover , S. A. ( 1997 ). Flexible modeling of the effects of serum cholesterol on coronary heart disease mortality . Amer. J. Epidemiology 145 : 714 – 729 . [CSA]
  • Abrahamowicz , M. , Du Berger , R. , Krewski , D. , Burnett , R. , Bartlett , G. , Tamblyn , R. M. , Leffondré , K. ( 2004 ). Bias due to aggregation of individual covariates in the Cox regression model . Amer. J. Epidemiology 160 : 696 – 706 . [CSA] [CROSSREF]
  • Akaike , H. ( 1973 ). Information theory as an extension of the maximum likelihood principle . In: Petrov , B. N. , Csaki , F. , eds. Second International Symposium on Information Theory . Budapest : Akademiai Kiado , pp. 267 – 281 .
  • Breslow , N. E. , Day , N. E. ( 1987 ). Statistical methods in cancer research . The Design and Analysis of Cohort Studies . IARC Scientific Publication no. 82 , 2 , Lyon, France : International Agency for Research on Cancer .
  • Brenner , H. , Blettner , M. ( 1997 ). Controlling for continuous confounders in epidemiologic research . Epidemiology 8 : 429 – 434 . [PUBMED] [INFOTRIEVE] [CSA] [CROSSREF]
  • Cakmak , S. , Burnett , R. T. , Krewski , D. ( 1999 ). Methods for detecting and estimating population threshold concentrations for air pollution-related mortality with exposure measurement error . Risk Anal. 19 : 487 – 496 . [PUBMED] [INFOTRIEVE] [CSA] [CROSSREF]
  • Cox , D. R. ( 1972 ). Regression models and life tables . J. Roy. Statist. Soc., Ser. B 34 : 187 – 220 . [CSA]
  • Durrleman , S. , Simon , R. ( 1989 ). Flexible regression models cubic splines . Statist. Med. 8 : 551 – 561 . [CSA]
  • Gray , R. J. ( 1992 ). Flexible methods for analyzing survival data using splines, with applications to breast cancer prognosis . J. Amer. Statist. Assoc. 87 : 942 – 951 . [CSA]
  • Greenland , S. ( 1995 ). Dose-response and trend analysis in epidemiology: alternatives to categorical analysis . Epidemiology 6 : 356 – 365 . [PUBMED] [INFOTRIEVE] [CSA]
  • Halpern , J. ( 1982 ). Maximally selected chi-square statistics for small samples . Biometrics 38 : 1017 . [CSA]
  • Hastie , T. , Tibshirani , R. ( 1990 ). Generalized Additive Models . New York : Chapman and Hall .
  • Hurvich , C. M. , Tsai , C. L. ( 1990 ). The impact of model selection on inference in linear regression . Amer. Statistician 44 : 214 – 217 . [CSA]
  • Kooperberg , C. , Stone , C. J. , Truong , Y. K. ( 1995 ). Hazard regression . J. Amer. Statist. Assoc. 90 : 78 – 94 . [CSA]
  • Leffondré , K. , Abrahamowicz , M. , Siemiatycki , J. , Rachet , B. (2002). Modeling smoking history: a comparison of different approaches. Amer. J. Epidemiology 156:813–823. [CSA] [CROSSREF]
  • Lipid Research Clinics Program. ( 1974 ). Manual of Laboratory Operations. National Institute of Health. NH Publications No. 1 , pp. 75 – 628 . [CSA]
  • Maclure , M. , Greenland , S. ( 1992 ). Tests for trend and dose-response: misinterpretations and alternatives . Amer. J. Epidemiology 135 : 96 – 104 . [CSA]
  • Mahmud , M. ( 2000 ). Impact of data dependent model selection on inference. Unpublished MSc thesis, Concordia University, Montreal, Canada .
  • Quantin , C. , Abrahamowicz , M. , Moreau , T. , Bartlett , G. , Mackenzie , T. , Tazi , M. A. , Lalonde , L. , Faivre , J. ( 1999 ). Variation over time of the effects of prognostic factors in a population-based study of colon cancer: comparison of statistical models . Amer. J. Epidemiology 150 : 1188 – 1200 . [CSA]
  • Ramsay , J. O. ( 1988 ). Monotone regression splines in action: with discussion . Statist. Sci. 3 : 425 – 461 . [CSA]
  • Ramsay , J. O. , Abrahamowicz , M. ( 1989 ). Binomial regression with monotone splines: a psychometric application . J. Amer. Statist. Assoc. 84 : 916 – 925 . [CSA]
  • Royston , P. , Altman , D. G. ( 1990 ). Regression using fractional polynomials of continuous covariates: parsimonious parametric modeling . Appl. Statist. 43 : 429 – 467 . [CSA]
  • Schulgen , G. , Lausen , B. , Olsen , J. H. , Schumacher , M. ( 1994 ). Outcome-oriented cut-points in analysis of quantitative exposure . Amer. J. Epidemiology 140 : 172 – 184 . [CSA]
  • Schwatrz , G. ( 1978 ). Estimating the dimension of a model . Ann. Statist. 6 : 461 – 464 . [CSA]
  • Sleeper , L. A. , Harrington , D. P. ( 1990 ). Regression splines in the Cox model with application to covariate effects in liver disease . J. Amer. Statist. Assoc. 85 : 941 – 949 . [CSA]
  • Zhao , L. P. , Kolonel , L. N. ( 1992 ). Efficiency loss from categorizing quantitative exposures into qualitative exposures in case-control studies . Amer. J. Epidemiology 136 : 464 – 474 . [CSA]

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.