Relative risk (RR, or risk ratio) and the odds ratio (OR) both compare how often an outcome occurs in two groups, and both equal 1 when there is no difference. They are often confused, and when the outcome is common they can be far apart: an OR of 3.14 read as "3 times the risk" overstates an RR of 2.50. This guide works through one example.
One example, both measures
In a cohort of 200, 30 of 100 smokers and 12 of 100 non-smokers developed the condition.
| Condition | No condition | Total | |
|---|---|---|---|
| Smokers | 30 | 70 | 100 |
| Non-smokers | 12 | 88 | 100 |
- Risk: 30/100 = 30% vs 12/100 = 12%.
- Relative risk = 30% / 12% = 2.50 (95% CI, 1.36-4.60).
- Risk difference = 30% − 12% = 18 percentage points.
- Odds: 30/70 = 0.429 vs 12/88 = 0.136.
- Odds ratio = 0.429 / 0.136 = 3.14 (95% CI, 1.50-6.58).
The OR is further from 1 than the RR because the outcome is common (30% and 12%). When the outcome is rare (below about 10% in both groups), the two are nearly equal.
Which one your study allows
- Cohort studies and trials measure risk directly: report the RR and the risk difference.
- Case-control studies fix the number of cases by design, so risks cannot be calculated: report the OR.
- Logistic regression produces ORs; report them as odds, or convert to adjusted risks if your journal asks.
How to report them
The condition developed in 30 of 100 smokers (30.0%) and 12 of 100 non-smokers (12.0%) (risk difference, 18.0 percentage points; relative risk, 2.50; 95% CI, 1.36-4.60).
Smoking was associated with higher odds of the condition (odds ratio, 3.14; 95% CI, 1.50-6.58).
Say "2.5 times the risk" only for an RR, and "3.14 times the odds" for an OR.
Mistakes reviewers catch
- Reading an OR as an RR when the outcome is common.
- Relative measures without absolute ones. An RR of 2.5 can mean 2% vs 0.8% or 50% vs 20%; give the risks or the risk difference.
- RR from a case-control study.
- No confidence intervals.
Let KyroStat do the write-up for you
KyroStat reports the measure your design allows, with the absolute risks and confidence intervals, and words each one correctly.
Frequently asked questions
What about hazard ratios? A hazard ratio compares event rates over time; see how to report a Cox regression.
How do I report an odds ratio in an APA journal? See how to report an odds ratio in APA 7.
What is the number needed to treat? 1 divided by the absolute risk difference; for the example, 1 / 0.18 = 5.6, so about 6. It is often reported alongside the RR in trials.