Relative Risk (Risk Ratio)

Relative risk, also called the risk ratio, is the ratio of the probability of an event occurring in an exposed or treated group to the probability of the same event occurring in an unexposed or control group. A relative risk of 1.0 indicates no difference between groups, values above 1.0 indicate increased risk in the exposed group, and values below 1.0 indicate reduced risk in the exposed group.

Relative risk is one of the most commonly reported measures of association in epidemiology, clinical trials, and public health research. It provides an intuitive measure of how much an exposure or intervention changes the probability of an outcome relative to a comparison group. Clinicians use relative risk to communicate treatment effects to patients, policymakers use it to evaluate the impact of public health interventions, and systematic reviewers pool relative risks across studies in meta analyses. Understanding the difference between relative and absolute measures of risk is critical for avoiding misinterpretation of research findings.

Relative risk is calculated by dividing the risk (incidence proportion) of the outcome in the exposed group by the risk in the unexposed group. If 20 out of 200 treated patients experience an adverse event (risk = 10%) and 40 out of 200 control patients experience the event (risk = 20%), the relative risk is 0.50, meaning the treatment cuts the risk in half.

Relative risk is directly interpretable in cohort studies and randomized controlled trials, where the incidence of the outcome can be calculated in each group. It cannot be calculated directly from case control studies, where participants are selected based on outcome status rather than exposure status; in those designs, the odds ratio is used instead, though it approximates the relative risk when the outcome is rare.

Confidence intervals for the relative risk are typically calculated on the log scale (because the log of the risk ratio follows a more symmetrical distribution) and then exponentiated. A 95% confidence interval that does not include 1.0 indicates a statistically significant association at the 0.05 level.

Relative risk should be interpreted alongside absolute risk measures. A treatment that reduces relative risk by 50% (RR = 0.50) may have dramatically different clinical implications depending on the baseline risk. If the baseline risk is 40%, the absolute risk reduction is 20 percentage points (number needed to treat = 5). If the baseline risk is 2%, the same relative risk reduction yields an absolute risk reduction of just 1 percentage point (number needed to treat = 100). Reporting both relative and absolute measures gives the most complete picture of the treatment's impact.

Use relative risk as the primary measure of association in cohort studies and randomized controlled trials when the outcome is binary. It is appropriate when the research question concerns how much an exposure or intervention changes the probability of the outcome relative to a comparison. Always report absolute risk measures alongside relative risk to provide clinical context. In case control studies, use the odds ratio rather than relative risk. In meta analyses of trials or cohort studies with binary outcomes, relative risk is often preferred over odds ratios because it is more intuitively interpretable, though the odds ratio is the measure available when the included studies are case control studies, where the relative risk cannot be directly estimated, and some analysts prefer it because, unlike the relative risk, its possible values are not limited by the baseline risk.

A common mistake is reporting relative risk without absolute risk, making it impossible for readers to assess the clinical significance of the finding. A 50% relative risk reduction sounds dramatic but may correspond to a trivially small absolute benefit. Another error is calculating relative risk from case control data, where the sampling design does not permit direct estimation of incidence. Researchers sometimes confuse relative risk with the odds ratio; while they are approximately equal when the outcome is rare, they diverge substantially when the outcome is common (above 10 to 20%). Finally, failing to adjust for confounders when reporting relative risk from observational data can produce biased estimates.

A cohort study follows 10,000 adults for five years to assess the relationship between statin use and incident myocardial infarction. Among 4,000 statin users, 120 experience a myocardial infarction (risk = 3.0%). Among 6,000 nonusers, 270 experience one (risk = 4.5%). The crude relative risk is 0.67 (95% CI: 0.54 to 0.82, calculated on the log scale), meaning the risk among statin users is 33% lower. The absolute risk difference is 1.5 percentage points, which would correspond to a number needed to treat of 67 for five years to prevent one event if the association were causal; because statin users may differ from nonusers in other ways, the relative risk should be adjusted for confounders before it is read as a treatment effect.