Build both measures from the same counts
In a fictional comparison, 60 of 100 people in one group experience an event, compared with 40 of 100 in another. The risks are 0.60 and 0.40, so the risk ratio is 1.5.
The odds are 60 divided by 40, or 1.5, in the first group. They are 40 divided by 60, or about 0.667, in the second. Dividing those odds gives an odds ratio of 2.25.
| Measure | Calculation | Result |
|---|---|---|
| Risk ratio | 0.60 / 0.40 | 1.5 |
| Odds ratio | (60/40) / (40/60) | 2.25 |
| Risk difference | 0.60 minus 0.40 | 0.20, or 20 percentage points |
The data did not change. The quantity being compared did.
Why “twice as likely” can mislead
Calling an odds ratio of two “twice the probability” generally changes its meaning. Converting an odds ratio into a risk ratio requires additional information, including an appropriate baseline risk, and adjusted models require particular care.
The CDC's measures-of-association guidance explains these distinctions and their relationship to study design. In a case-control study, the sampled numbers of cases and controls generally do not directly reveal population risks.
A reading habit that prevents the error
Before interpreting a headline number, find the measure's name in the methods or results. “Relative effect” is not specific enough. Then check the direction of the comparison and the outcome being counted.
The ratio also does not establish causation. The fictional arithmetic works whether the group difference arose from a causal effect, confounding, selection, or another process. Interpreting the design comes after identifying the quantity correctly.
