odds ratio
Meaning of odds ratio: Not a ratio of risks, though it is read as one constantly, and the gap between the two widens as an outcome becomes common.
Definition of odds ratio
An odds ratio compares the odds of an event in one group with the odds of the same event in another. Odds means the number of times something happens divided by the number of times it does not, which is not the same as a probability. A value of one means the two groups had the same odds, and values further from one mark a stronger association.
Why report odds rather than risk?
Some study designs cannot measure risk at all. In a case-control study, investigators start with people who already have the disease and add a comparison group of people who do not, deciding themselves how many of each to include. The proportion with disease in that sample is set by the researchers, so it reveals nothing about how common the disease actually is, and no real risk can be worked out from it. Odds of past exposure can still be compared between the two groups, and the answer comes out the same whether the calculation runs from exposure to disease or from disease to exposure. That symmetry is what makes the measure usable when risk is out of reach. The standard method for adjusting for other factors, logistic regression, also delivers its results in this form.
When does it mislead?
When the outcome is common. Odds and risk stay close while an event is rare, so the odds ratio then sits near the relative risk and reading one as the other does little harm. As the event becomes frequent the two separate, and the odds ratio always lies further from one. If half of one group and a quarter of the other have the outcome, the risk ratio is two while the odds ratio is three. Reporting that as a tripling of risk overstates what happened by half.
How do the three ratios compare?
| Measure | What it compares | Usual setting |
|---|---|---|
| Odds ratio | Odds in one group against odds in another | Case-control studies, logistic regression |
| Risk ratio | Risk in one group against risk in another | Cohort studies and clinical trials |
| Hazard ratio | How fast events accumulate over time | Survival analysis |
The number alone is incomplete whichever measure it is. The same value can come from a large study or a tiny one, and only the range of uncertainty reported beside it shows how far the data narrow the possibilities. A range that includes one leaves no difference among the plausible answers.
Also known as
Used in a sentence
The odds ratio for prior exposure was reported with a wide confidence interval.
Good to know
An odds ratio is read as a risk ratio far more often than it should be, since the two agree only while the outcome is uncommon, and the odds ratio always lies further from one when it is not.