Cited by 1,066Statistical Methods in EpidemiologyStatistical Methods and ApplicationsAdvanced Causal Inference Techniques

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

Royston, P., Ambler, G., Sauerbrei, W.·1999·International Journal of Epidemiology

DOI 10.1093/ije/28.5.964

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Abstract

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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Authors: Royston, P., Ambler, G., & Sauerbrei, W.
Affiliations: Imperial College London (GB)
Hammersmith Hospital (GB)
University of Freiburg (DE)
ORCID: Royston, P.
Ambler, G.
Sauerbrei, W.
Venue: International Journal of Epidemiology
Publisher: Oxford University Press (OUP)
Published: 1999-10-01
Volume: 28
Issue: 5
Pages: 964-974
ISSN: 0300-5771 (ISSN-L)
1464-3685
DOI: 10.1093/ije/28.5.964
OpenAlex: W2105087430
Cited by: 1,066
References: 44
Citations by year: 2026: 15 · 2025: 26 · 2024: 30 · 2023: 31 · 2022: 36 · 2021: 51 · 2020: 51 · 2019: 41 · 2018: 67 · 2017: 80 · 2016: 46 · 2015: 66 · 2014: 63 · 2013: 67 · 2012: 56
FWCI: 8.54
Type: journal article
Language: en
Open access: closed
Locations: International Journal of Epidemiology (publishedVersion)
PubMed (publishedVersion)
UCL Discovery (University College London) (submittedVersion)
FreiDok plus (Universitätsbibliothek Freiburg) (submittedVersion)
Funders: Wellcome Trust
Topics: Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
Keywords: fractional polynomials, risk transformation, risk curves, confounding variables, nonparametric regression, British civil servants
MeSH terms: Coronary Disease, Cross-Sectional Studies, Epidemiologic Methods, United Kingdom, Humans, Male, Models, Cardiovascular, Mortality, Neoplasms, Prospective Studies, Risk Factors, Sensitivity and Specificity, Linear Models, Odds Ratio, Risk Assessment, Stroke

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

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