Fractional polynomial model selection procedures: Investigation of type I error rate

Royston and Altman have demonstrated the usefulness of fractional polynomials in regression modelling, and have suggested model selection procedures for choosing appropriate fractional polynomial transformations. We investigate the performance of these procedures with particular regard to overfitting. We find the Type I error rates to be considerably in excess of their nominal value. We propose improvements which we show by simulation work reasonably well. We conclude that with the modifications, chi (2) or F approximations to likelihood ratio statistics to compare fractional polynomial models are adequate for practical purposes.