Improving the robustness of fractional polynomial models by preliminary covariate transformation: A pragmatic approach

Fractional polynomials have been found useful in univariate and multivariable non-linear regression analysis. As with many flexible regression models, they may be prone to distortion of the fitted function caused by values with high leverage at either extreme of the covariate distribution. Furthermore, fractional polynomial functions are not invariant to a change of origin of the covariate. A new approach, based on a preliminary, almost-linear transformation of a covariate, is proposed. The transformation is approximately linear within the bulk of the observations and tapers smoothly to a truncation of the extremes. It incorporates a predefined shift of the origin away from zero. Empirical studies show that this transformation is effective in reducing extreme leverages. In two real datasets, it is shown its use can result in more sensible final models.