Adding local components to global functions for continuous covariates in multivariable regression modeling

When global techniques, based on fractional polynomials (FPs), are employed for modeling potentially nonlinear effects of several continuous covariates on a response, accessible model equations are obtained. However, local features might be missed. Therefore, a procedure is introduced, which systematically checks model fits, obtained by the multivariable fractional polynomial (MFP) approach, for overlooked local features. Statistically significant local polynomials are then parsimoniously added. This approach, called MFP + L, is seen to result in an effective control of the Type I error with respect to the addition of local components in a small simulation study with univariate and multivariable settings. Prediction performance is compared with that of a penalized regression spline technique. In a setting unfavorable for FPs, the latter outperforms the MFP approach, if there is much information in the data. However, the addition of local features reduces this performance difference. There is only a small detrimental effect in settings where the MFP approach performs better. In an application example with children's respiratory health data, fits from the spline-based approach indicate many local features, but MFP + L adds only few significant features, which seem to have good support in the data. The proposed approach may be expected to be superior in settings with local features, but retains the good properties of the MFP approach in a large number of settings where global functions are sufficient.