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International Journal of Epidemiology, Vol 28, 964-974, Copyright © 1999 by International Epidemiological Association

ARTICLES

The use of fractional polynomials to model continuous risk variables in epidemiology

P Royston, G Ambler and W Sauerbrei
Department of Medical Statistics & Evaluation, Imperial College School of Medicine, London, UK. proyston@ic.ac.uk

BACKGROUND: The traditional method of analysing continuous or ordinal risk factors by categorization or linear models may be improved. METHODS: We propose an approach based on transformation and fractional polynomials which yields simple regression models with interpretable curves. We suggest a way of presenting the results from such models which involves tabulating the risks estimated from the model at convenient values of the risk factor. We discuss how to incorporate several continuous risk and confounding variables within a single model. The approach is exemplified with data from the Whitehall I study of British Civil Servants. We discuss the approach in relation to categorization and non-parametric regression models. RESULTS: We show that non-linear risk models fit the data better than linear models. We discuss the difficulties introduced by categorization and the advantages of the new approach. CONCLUSIONS: Our approach based on fractional polynomials should be considered as an important alternative to the traditional approaches for the analysis of continuous variables in epidemiological studies.
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