Odds ratios, risk ratios and hazard ratios: which to report
The three are routinely described as interchangeable and are not. Reporting the wrong one, or interpreting it as though it were another, changes what the paper claims.
All three compare two groups. They differ in what is being compared, and the difference matters most exactly where it is most often ignored — when the outcome is common.
Risk ratio
The probability of the outcome in the exposed group divided by the probability in the unexposed. It is what most readers assume they are being told, and the quantity most clinicians can act on: "twice as likely" means what it sounds like.
Estimable directly from cohort and trial data.
Odds ratio
The odds of the outcome — probability divided by one minus probability — compared between groups.
It approximates the risk ratio only when the outcome is rare. As the baseline risk rises, the odds ratio moves further from the risk ratio, always away from 1. An odds ratio of 2.0 with a 40 percent baseline risk corresponds to a risk ratio of about 1.4, and describing it as "twice the risk" overstates the effect substantially.
It exists because case-control designs can estimate it and cannot estimate risk, and because logistic regression produces it. Neither is a reason to interpret it as a risk ratio.
Hazard ratio
The ratio of instantaneous event rates over follow-up, from survival analysis. It uses time-to-event and handles censoring, which the other two discard.
Two cautions. It assumes proportional hazards — a constant ratio over time — and that assumption should be checked and reported rather than asserted. And a hazard ratio is not a risk ratio: it describes rates among those still at risk at each moment, which is not the same as the cumulative probability of the event.
Practical rules
- Report the risk ratio and the absolute risks when the design allows it. A relative effect without a baseline risk is uninterpretable clinically.
- Use the odds ratio when the design requires it, and say so. Do not describe it in the language of risk.
- Use the hazard ratio when timing matters and follow-up is incomplete, and check proportional hazards.
- Always give the absolute difference somewhere. A 50 percent relative reduction of a 0.2 percent risk is a different clinical conversation from a 50 percent reduction of a 20 percent risk, and only the absolute numbers distinguish them.
Frequently asked questions
What is the difference between an odds ratio and a risk ratio?
A risk ratio compares probabilities; an odds ratio compares odds. They approximate each other only when the outcome is rare. An odds ratio of 2.0 with a 40 percent baseline risk corresponds to a risk ratio of about 1.4, so describing it as "twice the risk" substantially overstates the effect.
Is a hazard ratio the same as a risk ratio?
No. A hazard ratio compares instantaneous event rates among those still at risk at each moment, which is not the cumulative probability of the event. It also assumes proportional hazards, an assumption that should be checked and reported.
Which ratio should I report?
Report the risk ratio and the absolute risks where the design allows. Use an odds ratio when the design requires it and do not describe it in the language of risk. Always give the absolute difference somewhere: a relative effect without a baseline risk cannot be interpreted clinically.