Use relative risk when risks can be directly estimated, such as in cohorts and trials. Odds ratios are standard in case-control studies and logistic regression.
The 2 by 2 table
| Outcome | No outcome | |
|---|---|---|
| Exposed | a | b |
| Unexposed | c | d |
RR = [a / (a + b)] / [c / (c + d)]OR = (a × d) / (b × c)How interpretation differs
An RR of 2 means the exposed group had twice the risk of the outcome. An OR of 2 means the odds of the outcome were twice as high. Risk and odds are not interchangeable, especially when the outcome is common.
Values above 1 indicate a positive association, values below 1 indicate a negative or potentially protective association, and 1 indicates no association on the ratio scale.
Worked example
Among 100 exposed people, 30 develop disease. Among 100 unexposed people, 10 develop disease.
- RR = 0.30 / 0.10 = 3.0
- OR = (30 × 90) / (70 × 10) = 3.86
The odds ratio is farther from 1 because the outcome is not rare. Reporting it as “3.86 times the risk” would be incorrect.
Which measure should you use?
| Design | Preferred approach |
|---|---|
| Cohort study | Relative risk or incidence rate ratio |
| Randomized trial | Relative risk, risk difference, and number needed to treat when suitable |
| Case-control study | Odds ratio |
| Logistic regression | Adjusted odds ratio |
| Cross-sectional study | Prevalence ratio is often easier to interpret; prevalence odds ratio may overstate association |
Interpretation cautions
- Association does not prove causation.
- Confounding, selection bias, and information bias can distort both measures.
- Report confidence intervals, not only point estimates.
- Consider absolute risks or risk differences to communicate public health impact.
Use the calculators
If your exposed and unexposed denominators are known, use the Relative Risk Calculator to estimate the risk ratio from a 2 by 2 table. If your study selected participants by case and control status, use the Odds Ratio Calculator instead.
For students and field teams, a helpful workflow is to first choose the design with the Study Design Selector, then calculate the measure that matches that design.
References
Rothman KJ, Greenland S, Lash TL. Modern Epidemiology. 3rd ed.
Viera AJ. Odds ratios and risk ratios: what's the difference and why does it matter? South Med J. 2008;101(7):730-734.