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The Stata Journal
Volume 7 Number 1: pp. 45-70



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Multivariable modeling with cubic regression splines: A principled approach

Patrick Royston
UK Medical Research Council
London, UK
patrick.royston@ctu.mrc.ac.uk
Willi Sauerbrei
University Medical Center
Freiburg, Germany
Abstract.   Spline functions provide a useful and flexible basis for modeling relationships 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 fractional 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 predictor 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.
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View all articles with these keywords: mvrs, uvrs, splinegen, multivariable analysis, continuous predictor, regression spline, model building, goodness of fit, choice of scale

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