Few statistical concepts generate as much confusion in clinical research as the difference between the odds ratio (OR) and relative risk (RR). Both are measures of association that quantify the relationship between an exposure (a risk factor, a treatment, a characteristic) and a health outcome (a disease, a complication, a recovery). However, they measure that relationship in fundamentally different ways, are calculated in different contexts, and their interpretation requires precautions that, when ignored, can lead to erroneous clinical conclusions. For researchers in medicine, nursing, and physiotherapy, understanding these differences is not a technical detail but an essential competency for reading and producing quality scientific literature.
The confusion between OR and RR is not a problem exclusive to students: studies that have analyzed literature published in top-tier medical journals have found that a considerable proportion of articles incorrectly interpret odds ratios as if they were relative risks. This error can be particularly serious when the prevalence of the outcome is high, because in those cases the OR considerably overestimates the magnitude of the association relative to the RR. Clarifying these concepts, with concrete clinical examples, is the purpose of this article. If you need to compute the OR and RR (with risk difference, NNT and confidence intervals) from your 2×2 table, you can do it in our odds ratio and risk ratio calculator.
Risk, odds, and their differences
To understand measures of association, one must first distinguish between risk and odds at the individual level. Risk (or probability) of an event is the number of people who experience the event divided by the total number of people at risk. If in a group of 100 surgical patients 20 develop a postoperative infection, the risk of infection is 20/100 = 0.20 (or 20%). Odds, on the other hand, are the number of people who experience the event divided by the number of people who do not experience it: 20/80 = 0.25. When the event is rare (low prevalence), risk and odds are numerically similar. When the event is frequent, they diverge significantly.
Relative risk compares the risk of the event between two groups by dividing one by the other. If the risk of infection in patients receiving antibiotic prophylaxis is 5% and in those not receiving it is 20%, the RR = 0.05/0.20 = 0.25. This means that patients with prophylaxis have a risk of infection that is 25% of the risk without prophylaxis, or in other words, prophylaxis reduces the risk by 75%. This interpretation is direct and intuitive, which explains the widespread preference for RR when the study design permits it.
The odds ratio compares the odds of the event between two groups. Following the same example, the odds of infection with prophylaxis are 5/95 = 0.053, and without prophylaxis 20/80 = 0.25. The OR = 0.053/0.25 = 0.21. The OR (0.21) is smaller than the RR (0.25), which illustrates that when the outcome is relatively frequent (20% in the control group), the OR exaggerates the magnitude of the association relative to the RR. If the infection were very rare (for example, 1% vs 0.25%), the OR and the RR would be virtually identical.
When to use each measure
The choice between OR and RR does not depend on the researcher's preference but on the study design. In cohort studies (prospective or retrospective) and in randomized clinical trials, where the incidence of the event in each group can be calculated directly, the RR is the measure of choice because it is more intuitive and does not overestimate the association. In case-control studies, where participants are selected based on the outcome (cases with the disease and controls without it) and the actual incidence cannot be calculated, the OR is the only valid measure of association. This limitation of case-control studies arises because the proportion of cases and controls is determined by the researcher and therefore does not reflect the true prevalence of the disease in the population.
In logistic regression, the measure of association obtained is always an OR, regardless of the study design. This creates a paradoxical situation: many cohort studies or clinical trials use logistic regression as their analytic technique and report ORs, when in reality they could (and should) report RRs using alternatives such as Poisson regression with robust variance or log-binomial models. This practice is especially problematic when the outcome is frequent, because the reported OR can give an exaggerated impression of a treatment's efficacy or the magnitude of a risk factor.
In meta-analyses, the choice between OR and RR has additional implications. The OR has mathematical properties that facilitate its combination across studies (symmetry, invariance with respect to the reference group), which explains why many meta-analyses use it. However, the interpretation of the combined OR can be confusing for clinicians, which is why some authors recommend computing the meta-analysis with OR and then converting the result to RR using the mean baseline prevalence from the control group to facilitate communication of the findings.
Common interpretation errors
The most common and most serious error is interpreting an OR as if it were an RR. Stating that "exposed patients have double the risk" when the OR is 2.0 is only approximately correct if the prevalence of the outcome is below 10%. With higher prevalences, an OR of 2.0 corresponds to a noticeably lower RR. For example, if the baseline prevalence of the event is 30%, an OR of 2.0 corresponds approximately to an RR of 1.5. The practical rule is clear: the more frequent the outcome under study, the greater the discrepancy between OR and RR, and the more problematic the interpretation of the OR in terms of risk.
Another common error is reporting the relative risk reduction without mentioning the absolute risk reduction. An RR of 0.50 (50% relative reduction) sounds impressive, but its clinical meaning is very different if the baseline incidence of the event is 40% (absolute reduction of 20%, NNT = 5) or 0.4% (absolute reduction of 0.2%, NNT = 500). The relative reduction is identical in both cases, but the clinical relevance is radically different. Always reporting the absolute risk reduction and the number needed to treat (NNT) alongside relative measures is a transparency practice that the CONSORT and STROBE guidelines explicitly recommend. If you work with diagnostic tests, also consult our guide on sensitivity, specificity, and ROC curves and the sensitivity and specificity calculator to obtain the values with their confidence intervals.
It is also advisable to exercise caution when interpreting adjusted ORs from multivariable logistic regression models. These ORs represent the association between the variable of interest and the outcome "holding constant" the other variables in the model. However, the adjustment only controls for the variables included in the model, not for all possible sources of confounding. Moreover, in logistic models, ORs from different models (with different adjustment variables) are not directly comparable due to the phenomenon of non-collapsibility of the OR, a technical issue that does not affect the RR and that makes comparing nested models a more delicate task than it appears.
Practical applications in health sciences
In clinical and epidemiological research, the correct use and interpretation of these measures has direct consequences for decision-making. A physiotherapist reading a meta-analysis on the efficacy of a manual therapy technique needs to know whether the results are expressed as OR or RR to correctly interpret the magnitude of the effect. If that results paragraph is written in jargon you do not control, paste it into explain this paragraph and it comes back in plain language with a glossary of the technical terms, instead of having to reconstruct the whole method to understand one sentence. A nurse reviewing a clinical practice guideline must be able to assess whether the recommendations are based on relative or absolute risk reductions. A physician communicating the benefits and risks of a treatment to a patient has the responsibility to present the figures in a comprehensible and non-misleading way.
Training in the correct interpretation of these measures should be part of the core curriculum for all healthcare professions, not just epidemiologists and biostatisticians. At a time when clinical decision-making increasingly relies on quantitative evidence, the ability to critically read study results and communicate them precisely to patients is a competency that transcends disciplinary boundaries and directly contributes to the quality and safety of healthcare.