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Smoothing using fractional polynomials: an alternative to polynomials and splines in applied research

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Michael David Regier, R. David Parker

Published Online: May 19 2015

DOI: 10.1002/wics.1355

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The fractional polynomial regression model is an emerging tool in applied research. Overcoming inherent problems associated with a polynomial expansion and splines, fractional polynomial models provide an alternate approach for modeling nonlinear relationships. In this article, we introduce the univariable and multivariable fractional polynomial model and highlight important aspects of their construction. Because of the curvilinear nature of fractional polynomial models, functional tables and functional plots are emphasized for model interpretation. We present two examples to illustrate fractional polynomial models for their selection and interpretation in applied research. WIREs Comput Stat 2015, 7:275–283. doi: 10.1002/wics.1355 This article is categorized under: Statistical and Graphical Methods of Data Analysis > Density Estimation Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods Statistical and Graphical Methods of Data Analysis > Transformations

A selection of 16 curves for four specifications of q: (a) q = (−2, 1), (b) q = (−2, − 0.5), (c) q = (0, 3), and (d) q = (−2, − 2). For each plot, the 16 curves are specified using different coefficient values, β (i.e. a 4² design for the coefficients with levels {−3, − 1, 1, 3}).

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Rate ratio contour plot as a function of the baseline mean lithium level and changes in the mean lithium level.

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