Response

Abstract

We thank Drs. Royston, Sauerbrei, and Altman for their insightful comments into the relative strengths and weaknesses of several approaches to the modeling of continuous data, and for pointing out the particular advantages of fractional polynomial regression over other modeling techniques. Admittedly, due to the practically unlimited number of possible models, we limited the scope of our analysis to categorical models and several types of spline models, both of which have a “local” character we wished to retain. As described by Royston et al., fractional polynomial models, or negative exponential models, have several advantages over categorical models and splines. Fractional polynomial models, unlike splines or categorical models, are free from the need to choose knots or category boundaries. By making appropriate choices of the fractional degrees of the polynomials, they can provide a wide variety of shapes. We wonder, however, if the results from a fractional polynomial regression model are substantially easier to interpret than the results of a spline analysis. Additionally, use of categorical models enable investigators to explore relationships that are not dose dependent and to more readily identify associations that are U-shaped in nature or for which a plateau effect may exist.