Multivariable Fractional Polynomials

The mfp package is a collection of R [3] functions targeted at the use of fractional polynomials (FP) for modelling the influence of continuous covariates on the outcome in regression models, as introduced by Royston & Altman (1994) [4] and modified by Sauerbrei & Royston (1999) [6]. The model may include binary, categorical or further continuous covariates which are included in the variable selection process but without need of FP transformation. It combines backward elimination with a systematic search for a ‘suitable’ transformation to represent the influence of each continuous covariate on the outcome. An application of multivariable fractional polynomials (MFP) in modelling prognostic and diagnostic factors in breast cancer is given by [6]. The stability of the models selected is investigated in [5]. Briefly, fractional polynomials models are useful when one wishes to preserve the continuous nature of the covariates in a regression model, but suspects that some or all of the relationships may be non-linear. At each step of a ‘backfitting’ algorithm MFP constructs a fractional polynomial transformation for each continuous covariate while fixing the current functional forms of the other covariates. The algorithm terminates when no more covariate is excluded and the functional forms of the continuous covariates do not change anymore.