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The use of fractional polynomials to model continuous risk variables in epidemiology
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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“NfL was entered as a linear predictor term after confirming linearity of the associations with fractional polynomial analyses (32).”
From A Method to Combine Neurofilament Light Measurements From Blood Serum and Plasma in Clinical and Population-Based Studies (2022) · cites this paper as [32]
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“Linearity in the logit was assessed with fractional polynomials (35).”
From Personality, Socioeconomic Status, and All-Cause Mortality in the United States (2010) · cites this paper as [35]
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Metadata
- Authors
- Royston, P., Ambler, G., & Sauerbrei, W.
- Affiliations
- Imperial College London (GB)
- Hammersmith Hospital (GB)
- University of Freiburg (DE)
- 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
- 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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