An odds ratio of 3 does not mean "three times the risk". With an outcome occurring in 40 % of the unexposed, the real risk ratio is <strong>1.67</strong>. OR and RR only resemble each other when the outcome is rare, and in health research it rarely is.
RR = OR / (1 − p₀ + p₀ · OR)
Risk is cases over total: 40 in 100 is 0.40. Odds are cases over non-cases: 40 over 60, that is 0.67. When the outcome is rare the two nearly coincide — 2 in 100 is a risk of 0.02 and odds of 0.0204 — and that is where the habit of treating them alike comes from.
When the outcome is common they stop coinciding, and the odds ratio departs from the risk ratio always in the same direction: away from 1. An OR above 1 is always larger than its RR; one below 1 is always smaller.
Which makes the OR especially misleading in studies of common things: anxiety prevalence, adherence, treatment dropout, passing a course.
Because logistic regression returns odds. That is not an author decision, it is the model output. In a case-control design the RR is not even estimable, because the design fixes how many cases there are.
And because the OR behaves well mathematically: it is symmetric with respect to how you define the outcome and does not depend on the sample prevalence. Those are real advantages.
What is not defensible is mistranslating it in the discussion: writing "were three times as likely" when what you have is an OR of 3 and a common outcome. At that point the error is no longer the model’s, it is the sentence’s.
Report the OR with its interval, which is what the model estimated, and add the absolute risk in each group. With those two numbers the reader can do the conversion themselves and grasp the real magnitude.
If the outcome is common and you want to talk about risk in the discussion, convert and say so: "the OR of 3 corresponds to an RR of 1.67 at the observed baseline risk of 40 %".
And if what you need is to pool that OR with studies reporting d, that is a different conversion: d and r has its own page, and OR to d goes through the Chinn formula.
All thirteen effect size conversions, grouped by what each one is for, are in the index.
If you use it in your thesis or in a paper, cite it so that readers of your Methods section know how the calculation was done.
Ciudad-Fernández, V. (2026). Odds ratio to risk ratio converter [Web application]. Ciudad Science. Retrieved October 14, 2026, from https://analisisdedatospsicologia.com/en/convert/odds-ratio-to-risk-ratio
For your Methods section: Odds ratios were converted into risk ratios from the risk in the unexposed group (Zhang & Yu, 1998), using the Ciudad Science odds ratio to risk ratio converter (Ciudad-Fernández, 2026).
@misc{ciudadfernandez2026convoddsratioariesgorelativo,
author = {Ciudad-Fern{\'a}ndez, V{\'i}ctor},
title = {{Odds ratio to risk ratio converter}},
year = {2026},
publisher = {Ciudad Science},
howpublished = {Web application},
url = {https://analisisdedatospsicologia.com/en/convert/odds-ratio-to-risk-ratio},
urldate = {2026-10-14},
note = {Accessed 2026-10-14},
}From the paper’s own frequency table: cases over total in the unexposed or control group. If the paper does not give it, the conversion cannot be done — and that alone is a reason to request it in review.
The classic rule is a baseline risk under 10 %. At p₀ = .01 and OR = 3 the RR is 2.94: the difference fits inside the rounding. At p₀ = .20 it is already 2.14 against 3.
There the OR is the correct estimator and the RR is not estimable, because the design fixes the proportion of cases. The conversion only makes sense if you know the baseline risk from another source, and then you have to say where it came from.
No. A hazard ratio is a ratio of instantaneous rates over time, not a ratio of odds. It looks similar and does not convert with this formula.