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.
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.