Many medical and social-science papers report an odds ratio (OR). Many readers, and quite a few press releases, then describe it as if it were a risk ratio (RR): "people with X were twice as likely to develop Y." Sometimes that's roughly right. Sometimes it overstates the effect a lot.
Risk and odds are different scales
Take 100 people, 20 of whom develop an outcome.
- Risk (probability) = 20 / 100 = 0.20
- Odds = 20 / 80 = 0.25
Risk compares cases with everyone. Odds compare cases with non-cases. For rare outcomes the two are nearly equal, because the number of non-cases is almost the whole group. For common outcomes they drift apart quickly: a risk of 0.5 corresponds to odds of 1.0, and a risk of 0.8 to odds of 4.0.
How the ratios diverge
Suppose the outcome occurs in 40% of an exposed group and 20% of an unexposed group.
- Risk ratio = 0.40 / 0.20 = 2.0
- Odds ratio = (0.40/0.60) / (0.20/0.80) = 0.667 / 0.25 = 2.67
The odds ratio is further from 1 than the risk ratio. This is always the case when the outcome is common: an OR exaggerates the effect if you read it as an RR. With an outcome that occurs in 2% vs. 1% of people, OR and RR are both about 2.0, so the confusion does little harm.
Why odds ratios are so common anyway
- Logistic regression naturally produces odds ratios, and it is the default tool for binary outcomes.
- Case-control studies sample people by outcome status, so the true risk in each group can't be estimated. The odds ratio is still valid in that design.
- Odds ratios have convenient mathematical properties (they are symmetric for the outcome and its absence).
These are good reasons to compute an OR. They are not reasons to describe it as "times as likely."
Practical advice
- Check how common the outcome is. Under roughly 10%, OR ≈ RR is a fair approximation. Above that, be careful.
- Look for absolute numbers. The proportions in each group tell you more than either ratio alone.
- Prefer risk ratios or risk differences when the design allows. Methods such as log-binomial or modified Poisson regression estimate them directly in cohort studies and trials.
- When you write, say "odds". "The odds were 2.7 times higher" is accurate; "2.7 times as likely" usually isn't.
The short version: odds and risk are two different scales. For rare outcomes they agree; for common outcomes the odds ratio makes effects look bigger than they are.
More research explainers: https://www.crushsci.com