Bias in odds ratios by logistic regression modelling and sample size
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BACKGROUND: In epidemiological studies researchers use logistic regression as an analytical tool to study the association of a binary outcome to a set of possible exposures. METHODS: Using a simulation study we illustrate how the analytically derived bias of odds ratios modelling in logistic regression varies as a function of the sample size. RESULTS: Logistic regression overestimates odds ratios in studies with small to moderate samples size. The small sample size induced bias is a systematic one, bias away from null. Regression coefficient estimates shifts away from zero, odds ratios from one. CONCLUSION: If several small studies are pooled without consideration of the bias introduced by the inherent mathematical properties of the logistic regression model, researchers may be mislead to erroneous interpretation of the results.
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Using maximum likelihood estimation yields only asymptotically unbiased estimates of individual coefficients.
“using maximum likelihood estimation, as is done for logistic regression and Cox proportional hazards regression for time to event outcomes, yields only asymptotically unbiased estimates of individual coefficients [23].”
From A calibration hierarchy for risk models was defined: from utopia to empirical data (2016) · cites this paper as [23]
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- Authors
- Nemes, S., Jonasson, J. M., Genell, A., & Steineck, G.
- Affiliations
- University of Gothenburg (SE)
- Karolinska Institutet (SE)
- Venue
- BMC Medical Research Methodology
- Published
- 2009-07-27
- Volume
- 9
- Issue
- 1
- Pages
- 56-56
- ISSN
- 1471-2288 (ISSN-L)
- PMC
- PMC2724427
- OpenAlex
- W2168885658
- Cited by
- 437
- References
- 18
- Citations by year
- 2026: 14 · 2025: 29 · 2024: 41 · 2023: 26 · 2022: 33 · 2021: 32 · 2020: 35 · 2019: 27 · 2018: 24 · 2017: 17 · 2016: 27 · 2015: 31 · 2014: 21 · 2013: 24 · 2012: 30
- FWCI
- 15.53
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- BMC Medical Research Methodology (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
- Funders
- Cancerfonden
- Vetenskapsrådet
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Keywords
- odds ratio bias, logistic regression, sample size, small sample bias, binary outcomes, simulation study
- MeSH terms
- Computer Simulation, Female, Humans, Pregnancy, Models, Statistical, Bias, Logistic Models, Odds Ratio, Sample Size
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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