Bayesian fractional polynomials

This paper sets out to implement the Bayesian paradigm for fractional polynomial models under the assumption of normally distributed error terms. Fractional polynomials widen the class of ordinary polynomials and offer an additive and transportable modelling approach. The methodology is based on a Bayesian linear model with a quasi-default hyper-g prior and combines variable selection with parametric modelling of additive effects. A Markov chain Monte Carlo algorithm for the exploration of the model space is presented. This theoretically well-founded stochastic search constitutes a substantial improvement to ad hoc stepwise procedures for the fitting of fractional polynomial models. The method is applied to a data set on the relationship between ozone levels and meteorological parameters, previously analysed in the literature

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

© Springer-Verlag Berlin Heidelberg 2002. 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