What is an odds ratio?

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.

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.