Posters · Glossary
What is an odds ratio?
An odds ratio compares the odds of an outcome in one group with the odds in another, where odds are the number with the outcome divided by the number without it. A value of 1 means no difference, above 1 means higher odds in the first group, and below 1 lower odds. It is not a risk ratio.
Odds ratios appear on posters from case control studies, logistic regression models and many trials, and they are routinely read as if they said how many times more likely something is. That reading is close enough when the outcome is rare and badly wrong when it is common.
Indunil Asanka · Co-founder
6 min read · Published
| Outcome | No outcome | Odds of the outcome | |
|---|---|---|---|
| Exposed | 60 | 40 | 60 divided by 40 = 1.5 |
| Unexposed | 30 | 70 | 30 divided by 70 = 0.43 |
| Odds ratio | 1.5 divided by 0.43 = 3.5, the same as (60 x 70) divided by (40 x 30) | ||
| Risk ratio for comparison | 60 percent | 30 percent | 0.60 divided by 0.30 = 2.0 |
Odds are not probabilities
Probability, or risk, is the number with the outcome divided by everyone. Odds are the number with the outcome divided by the number without it. If 60 of 100 people develop a condition, the risk is 60 percent but the odds are 60 to 40, or 1.5. Szumilas, in a short explainer in the Journal of the Canadian Academy of Child and Adolescent Psychiatry, defines the odds ratio as the odds that an outcome will occur given a particular exposure, compared with the odds of the outcome occurring in the absence of that exposure. The two scales agree closely only when the outcome is uncommon.
Reading the worked example
In the table, the exposed group's odds are 1.5 and the unexposed group's odds are about 0.43, so the odds ratio is 3.5. The risks are 60 and 30 percent, so the risk ratio is 2.0. Both numbers are correct, but they say different things. Saying the exposed group was 3.5 times as likely to have the outcome would overstate the difference, because they were twice as likely. The gap between the two measures grows as the outcome becomes more common, which is why the Cochrane Handbook warns against interpreting odds ratios as if they were risk ratios.
Why case control studies use it
A case control study starts with people who have the outcome and a comparison group who do not, then looks back at exposure. Because the researcher chooses how many cases and controls to include, the true risk in each exposure group cannot be calculated, so a risk ratio is not available. The odds ratio can still be estimated, because the odds of exposure among cases compared with controls equals the odds ratio for the outcome. The CDC's Principles of Epidemiology course notes that when the disease is rare, the odds ratio from a case control study approximates the risk ratio.
Adjusted odds ratios from logistic regression
Logistic regression, the usual model for yes or no outcomes, produces odds ratios for each variable, adjusted for the others in the model. That is why so many observational studies report adjusted odds ratios even when they are not case control designs. On a poster, name what the odds ratio was adjusted for, such as age, sex and baseline severity, and report the crude figure too when the difference between them is informative. A large change after adjustment tells readers that confounding mattered. Interaction terms and continuous predictors need extra care in the wording, since an odds ratio per one unit of age means little until it is scaled to a meaningful step such as ten years.
Common mistakes
The most common error is describing an odds ratio of 2.8 as 2.8 times the risk when the outcome affects a large share of people. Another is presenting an odds ratio without its confidence interval, which gives no sense of precision. Reporting odds ratios below one as percentages, such as a 40 percent reduction for an odds ratio of 0.6, invites the same risk confusion. Mixing up the reference group, so that an odds ratio of 0.4 is read as 2.5 in the other direction, is also frequent. Finally, many boards omit the underlying counts, leaving readers unable to check the arithmetic.
Where it shows up in the poster builder
An odds ratio is typically the key number on an observational or trial poster, with the interval in the detail line below it. Key number blocks appear on 27 of the 40 layouts, so a value such as OR 2.8 can sit above its interval of 1.9 to 4.1. Chart figures take categories and values with no interval whiskers, so a chart can compare the proportions in each group while the odds ratio and its interval stay in words. Put the counts, the odds ratio, the interval and what it was adjusted for in the brief, since the generator fills every number from what it is given.
Questions people ask
Can I convert an odds ratio into a risk ratio?
Approximately, if you know the risk in the reference group. Formulas exist that use that baseline risk to convert an odds ratio into an estimated risk ratio, and they matter most when the outcome is common. Without the baseline risk the conversion is not possible. Where the design allows, report risks and a risk ratio directly instead of converting afterwards.
What does an odds ratio of 0.5 mean?
It means the odds of the outcome in the first group are half the odds in the reference group. If the outcome is rare, that is close to half the risk. If the outcome is common, the reduction in risk is smaller than half. State it as lower odds on the poster rather than a percentage reduction in risk, unless the outcome is rare.
Why is the confidence interval for an odds ratio not symmetrical?
Odds ratios are calculated on a log scale, where the interval is symmetrical, then converted back. On the ordinary scale that makes the upper limit further from the estimate than the lower limit, such as 2.6 with an interval of 1.8 to 3.7. It is expected, not an error, and charts of odds ratios are often drawn on a log axis for the same reason.
When is an interval for an odds ratio considered significant?
When a 95 percent interval excludes 1, the association is statistically significant at the 5 percent level. An interval such as 0.9 to 2.4 includes 1, so the data are compatible with no association as well as a sizeable one. Report the interval itself and discuss what range of effects it allows, rather than only the significant or not verdict.
Is a high odds ratio proof of causation?
No. An odds ratio measures association. In observational studies it can be produced by confounding, selection of cases and controls, or recall bias, where people with a condition remember exposures differently. Causal claims need a design that addresses those threats, plus consistency with other evidence. Word the conclusion as an association unless the design justifies more.
What sample size does an odds ratio need?
Enough events in each group for a stable estimate. With very few cases in one cell of the 2x2 table, the odds ratio becomes unstable and its interval very wide, sometimes running from below one to double figures. In logistic regression, too few outcome events per variable in the model also produces unreliable estimates, so plan the sample around the number of events.
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- What is a rate ratio?What is a rate ratio: the incidence rate in one group divided by the rate in another, using person time. How it differs from a risk ratio and an odds ratio.
- What is effect size?What is effect size: how big a difference or association is, not whether it passed a significance test. Cohen's d, risk and odds ratios, and how to report them.
- Cohort vs case-control studyCohort vs case control study: a cohort follows people from exposure to outcome, a case control study starts at the outcome and looks back. What each estimates.
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