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Multivariable modeling with cubic regression splines: A principled approach

Author

Listed:
  • Patrick Royston

    (Cancer Group, MRC Clinical Trials Unit)

  • Willi Sauerbrei

    (University Medical Center, Freiburg)

Abstract

Spline functions provide a useful and flexible basis for modeling re- lationships with continuous predictors. However, to limit instability and provide sensible regression models in the multivariable setting, a principled approach to model selection and function estimation is important. Here the multivariable frac- tional polynomials approach to model building is transferred to regression splines. The essential features are specifying a maximum acceptable complexity for each continuous function and applying a closed-test approach to each continuous pre- dictor to simplify the model where possible. Important adjuncts are an initial choice of scale for continuous predictors (linear or logarithmic), which often helps one to generate realistic, parsimonious final models; a goodness-of-fit test for a parametric function of a predictor; and a preliminary predictor transformation to improve robustness. Copyright 2007 by StataCorp LP.

Suggested Citation

  • Patrick Royston & Willi Sauerbrei, 2007. "Multivariable modeling with cubic regression splines: A principled approach," Stata Journal, StataCorp LP, vol. 7(1), pages 45-70, February.
    • Handle: RePEc:tsj:stataj:v:7:y:2007:i:1:p:45-70
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    References listed on IDEAS

    as
    1. Patrick Royston & Gareth Ambler, 1999. "Multivariable fractional polynomials," Stata Technical Bulletin, StataCorp LP, vol. 8(43).
    2. Willi Sauerbrei, 1999. "The Use of Resampling Methods to Simplify Regression Models in Medical Statistics," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(3), pages 313-329.
    3. W. Sauerbrei & P. Royston, 1999. "Building multivariable prognostic and diagnostic models: transformation of the predictors by using fractional polynomials," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 162(1), pages 71-94.
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