Adaptive Fractional Polynomial Modeling in SAS

Regression predictors are usually entered into a model without transformation. However, it is not unusual for regression relationships to be distinctly nonlinear. Fractional polynomials account for nonlinearity through real-valued power transformations of primary predictors. Adaptive methods have been developed for searching through alternative fractional polynomials based on one or more primary predictors. A SAS macro called genreg (for general regression) is available from the author for conducting such analyses. It supports adaptive linear, logistic, and Poisson regression modeling of expected values and/or variances/dispersions in terms of fractional polynomials. Fractional polynomial models are compared using k-fold likelihood cross-validation scores and adaptively selected through heuristic search. The genreg macro supports adaptive modeling of both univariate and multivariate outcomes. It also supports adaptive moderation analyses based on geometric combinations, that is, products of transforms of primary predictors with possibly different powers, generalizing power transforms of interactions. Example analyses and code for conducting them are presented demonstrating adaptive fractional polynomial modeling.