Reviewed and revised 26 August 2015
- An odds ratio (OR) is a measure of association between an exposure and an outcome.
- The OR represents the odds that an outcome will occur given a particular exposure, compared to the odds of the outcome occurring in the absence of that exposure.
- odds are different to probability — odds is the ratio of the probability that the event of interest occurs to the probability that it does not
- don’t confuse odds with probability, and don’t confuse odds with odds ratio!
- odds ratio is not as intuitive as relative risk
USE OF ODDS RATIO
odds ratio gives an indication of the strength of association between groups
- commonly used in meta-analysis
- must be used in case-control studies rather than relative risk (RR) as there is no information on the numbers of all exposed and non-exposed
- used in logistic regression
- the odds of the disease in exposed over the odds of the non-exposed
OR = odds of disease in exposed / odds of disease in the non-exposed
= (a/b) / (c/d)
- OR is not equivalent to risk
- OR is approximately the same as the relative risk (RR) when the outcome is rare (approx <10%)
- OR <1 tends to underestimate RR, OR >1 tends to overestimate RR; degree of mis-estimation increases at higher base event rates
- OR of 1 means no association
- if OR is reported with a CI which includes 1 then the OR is not significant
References and Links
- Bland JM, Altman DG. Statistics notes. The odds ratio. BMJ. 2000 May 27;320(7247):1468. PMC1127651.
- Pepe MS, Janes H, Longton G, Leisenring W, Newcomb P. Limitations of the odds ratio in gauging the performance of a diagnostic, prognostic, or screening marker. Am J Epidemiol. 2004 May 1;159(9):882-90. PMID: 15105181.
- Szumilas M. Explaining odds ratios. J Can Acad Child Adolesc Psychiatry. 2010 Aug;19(3):227-9. PMC2938757.
- CSM — BMJ Statistics Notes
- When can odds ratios mislead? BMJ 1998;316:989