Odds ratio

Reviewed and revised 26 August 2015

OVERVIEW

• 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

CALCULATION

• 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)

INTERPRETATION

• 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

Journal articles

• 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