What is an odds ratio?

• A. The ratio of probabilities of an event between two groups.
• B. The difference in probabilities of an event between two groups.
• C. The ratio of the odds of an event occurring in group A versus group B.
• D. The correlation between treatment and outcome.

Answer: (C)

An odds ratio tells you how the odds of an event compare between two groups. Odds are the chances of the event happening relative to it not happening, calculated as p/(1−p) where p is the probability of the event. To get the odds ratio, you compute the odds in each group, then form the ratio of those odds.

For example, if 20% of group A experience the event, the odds in A are 0.20/0.80 = 0.25. If 10% in group B experience it, the odds in B are 0.10/0.90 ≈ 0.111. The odds ratio is 0.25 divided by 0.111, about 2.25, meaning the event’s odds are more than twice as high in group A as in group B.

This is different from the ratio of probabilities (which would be a relative risk like 0.20/0.10 = 2.0) and from the difference in probabilities (0.20 − 0.10 = 0.10). It’s also not a measure of correlation.