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Linear, nonlinear or categorical: how to treat complex associations in regression analyses? Polynomial transformations and fractional polynomials

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International Journal of Public Health

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References

  • Becher H (2005) General principles of data analysis: continuous covariables in epidemiological studies. In: Ahrens W, Pigeot I (eds) Handbook of epidemiology. Springer, Heidelberg, p 595–624

  • Beck N, Jackman S (1998) Beyond linearity by default: generalized additive models. Am J Political Sci 42(2):596–627

    Article  Google Scholar 

  • Burnham KP, Anderson DR (2004) Multimodel inference—understanding AIC and BIC in model selection. Sociol Methods Res 33(2):261–304

    Article  Google Scholar 

  • Maclure M, Greenland S (1992) Tests for trend and dose response: misinterpretations and alternatives. AmJ Epidemiol 135(1):96–104

    CAS  Google Scholar 

  • May S, Bigelow C (2005) Modeling nonlinear dose-response relationships in epidemiologic studies: statistical approaches and practical challenges. Dose Response 3(4):474–490

    Article  Google Scholar 

  • Rothman KJ, Greenland S, Lash T (2008) Modern epidemiology, vol 4. Lippincott Williams & Wilkins, Philadelphia

    Google Scholar 

  • Royston P, Sauerbrei W (2004) A new approach to modelling interactions between treatment and continuous covariates in clinical trials by using fractional polynomials. Stat Med 23(16):2509–2525

    Article  PubMed  Google Scholar 

  • Royston P, Sauerbrei W (2007) Improving the robustness of fractional polynomial models by preliminary covariate transformation: a pragmatic approach. Comput Stat Data Anal 51(9):4240–4253

    Article  Google Scholar 

  • Royston P, Sauerbrei W (2008) Multivariable model building: a pragmatic approach to regression analysis based on fractional polynomials for modelling continuous variables. John Wiley & Sons, Chichester

  • Royston P, Ambler G, Sauerbrei W (1999) The use of fractional polynomials to model continuous risk variables in epidemiology. Int J Epidemiol 28(5):964–974

    Article  PubMed  CAS  Google Scholar 

  • Royston P, Altman DG, Sauerbrei W (2006) Dichotomizing continuous predictors in multiple regression: a bad idea. Stat Med 25(1):127–141

    Article  PubMed  Google Scholar 

  • Royston P, Sauerbrei W, Becher H (2010) Modelling continuous exposures with a ‘spike’ at zero: a new procedure based on fractional polynomials. Stat Med 29(11):1219–1227

    PubMed  Google Scholar 

  • Sauerbrei W, Meier-Hirmer C, Benner A, Royston P (2006) Multivariable regression model building by using fractional polynomials: description of SAS, STATA and R programs. Comput Stat Data Anal 50(12):3464–3485

    Article  Google Scholar 

  • Schmidt CO, Ittermann T, Schulz A, Grabe HJ, Baumeister SE (2012) Linear, nonlinear or categorical: how to treat complex associations in regression analyses? Splines and nonparametric approaches. Int J Public Health (IJPH-11-41)

  • Volzke H et al (2010) Cohort profile: the study of health in Pomerania. Int J Epidemiol 40(2):294–307

    Article  PubMed  Google Scholar 

  • Wingenfeld K et al (2010) The German version of the Childhood Trauma Questionnaire (CTQ): preliminary psychometric properties]. Psychother Psychosom Med Psychol 60(11):442–450

    Article  PubMed  Google Scholar 

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Acknowledgments

SHIP is part of the Community Medicine Research net of the University of Greifswald, Germany, which is funded by the Federal Ministry of Education and Research (Grants no. 01ZZ9603, 01ZZ0103, and 01ZZ0403), the Ministry of Cultural Affairs and the Social Ministry of the Federal State of Mecklenburg-West Pomerania. This work was also funded by the German Research Foundation (DFG: GR 1912/5-1).

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Correspondence to Carsten Oliver Schmidt.

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Schmidt, C.O., Ittermann, T., Schulz, A. et al. Linear, nonlinear or categorical: how to treat complex associations in regression analyses? Polynomial transformations and fractional polynomials. Int J Public Health 58, 157–160 (2013). https://doi.org/10.1007/s00038-012-0362-0

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  • DOI: https://doi.org/10.1007/s00038-012-0362-0

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