Determination of Functional Relationships for Continuous Variables by Using a Multivariable Fractional Polynomial Approach

Abstract

Determination of a transformation which better describes the functional relationship between the outcome and a continuous covariate may substantially improve the fit of a model. The so-called fractional polynomials approach was proposed to investigate in a systematic fashion possible improvements in fit by the use of non-linear functions. The approach may be used to combine variable selection with the determination of functional relationships for continuous regressors in a multivariable setting, and is applicable to a wide range of general regression models. We will demonstrate some advantages of this flexible family of parametric models by discussing several aspects of modelling the continuous risk factors in a large cohort study. We will also use data halving and the bootstrap to investigate whether the considerable flexibility of the fractional polynomials approach causes instability in the selected functions.