# Odds ratio

An odds ratio compares the odds of an outcome between two groups. Odds are events divided by non-events, not by the total. If 20 of 100 people reach the outcome, the odds are 20/80, that is 0.25, while the risk is 20/100, that is 0.20. It is the native output of logistic regression and the only valid effect measure in case-control studies, where sampling on the outcome makes incidence unknowable. It also stays the same when exposure and outcome are swapped, which is mathematically convenient and clinically irrelevant. The failure mode is interpretation. An odds ratio always lies further from 1.0 than the matching risk ratio, and the gap grows with the baseline rate. Take a control risk of 40% and a treated risk of 20%. The risk ratio is 0.50, a 50% reduction. The odds ratio is 0.20/0.80 divided by 0.40/0.60, which equals 0.375. Reported as a 62% reduction, it overstates the benefit by a quarter. Zhang and Yu published a correction formula in 1998, and Grant later showed how to convert an odds ratio into a plausible range of risk ratios. In nutrition and longevity epidemiology, outcomes such as metabolic syndrome, insomnia or frailty are common, so odds ratios from cross-sectional surveys inflate easily. Check the baseline rate before trusting the size.

## Sources

- Bland JM, Altman DG. (2000). Statistics Notes: The odds ratio. BMJ. https://doi.org/10.1136/bmj.320.7247.1468
- Norton EC, Dowd BE, Maciejewski ML. (2018). Odds ratios: current best practice and use. JAMA. https://doi.org/10.1001/jama.2018.6971
- Grant RL. (2014). Converting an odds ratio to a range of plausible relative risks for better communication of research findings. BMJ. https://doi.org/10.1136/bmj.f7450
- Zhang J, Yu KF. (1998). What's the relative risk? A method of correcting the odds ratio in cohort studies of common outcomes. JAMA. https://doi.org/10.1001/jama.280.19.1690

---

_Canonical: https://longevity-germany.com/en/glossary/odds-ratio · Part of Longevity Cities · Updated 2026-08-25_