Relative Risk (RR)

Relative risk (RR), also called the risk ratio, is the ratio of the risk (cumulative incidence) of an outcome in an exposed or treated group to the risk of that same outcome in an unexposed or control group, over a defined follow-up period. It is one of the primary measures epidemiologists and trialists use to express how much an exposure or intervention changes the probability of an event — and it is only valid to calculate from study designs that observe true incidence, which rules out the case-control design used for many rare-outcome studies.

Formula

RR = Risk in the exposed/treatment group ÷ Risk in the unexposed/control group, where each “risk” is a cumulative incidence proportion (number who had the event ÷ number followed at the start of the period):

	Outcome occurred	Outcome did not occur	Total
Exposed / treated	A	B	A + B
Unexposed / control	C	D	C + D

RR = [A / (A + B)] ÷ [C / (C + D)]. Unlike an odds ratio, both numerator and denominator here are true risks (proportions of a known population at risk), not odds — which is exactly why RR requires a design where the group totals (A+B and C+D) reflect real population sizes rather than a sampling ratio the investigator chose.

Worked example

A randomized trial follows 2,000 participants for one year: 1,000 receive a new antihypertensive, 1,000 receive placebo.

	Stroke	No stroke	Total
Treatment	40	960	1,000
Placebo	80	920	1,000

Risk(treatment) = 40/1,000 = 4%. Risk(placebo) = 80/1,000 = 8%. RR = 0.04 / 0.08 = 0.50. Patients on treatment had half the stroke risk of patients on placebo — a 50% relative risk reduction (1 − RR). Note this single number says nothing about the absolute size of the benefit: going from 8% to 4% risk (RR = 0.50) prevents 4 events per 100 people treated, while going from 0.08% to 0.04% risk is the same RR = 0.50 but prevents only 0.04 events per 100 people treated. See Absolute Risk Reduction, Relative Risk Reduction, and Number Needed to Treat for how to convert a relative measure into that absolute, clinically actionable number.

Interpreting the value

• RR = 1.0 — no association; the outcome is equally likely in both groups.
• RR > 1.0 — the exposure is associated with increased risk (e.g. RR = 5.0 means five times the risk).
• RR < 1.0 — the exposure is associated with decreased (protective) risk (e.g. RR = 0.50 means half the risk).

Relative risk is symmetric around 1.0 in direction but not in scale: RR values below 1 are compressed into the 0–1 range while values above 1 are unbounded, which is why a “reduced risk” RR is often reported instead as its complement, the relative risk reduction (1 − RR), or via the reciprocal framing (comparing the unexposed group to the exposed group) when that reads more naturally.

Relative risk vs. odds ratio

Relative risk and odds ratio answer the same conceptual question — how much more (or less) likely is the outcome in one group versus another — but they are calculated from different quantities and are not interchangeable choices of convenience. Cohort studies and randomized trials observe a population’s true incidence (they know how many people were “at risk” at the start), so they can validly calculate relative risk. Case-control studies fix the ratio of cases to controls by study design rather than observing true population incidence, so incidence and relative risk cannot be validly calculated from a standard case-control sample; an odds ratio (the odds of exposure among cases versus controls) is used instead. Under the “rare disease assumption” (the outcome affects well under 10% of the population), the odds ratio closely approximates the relative risk that a cohort study of the same population would show — but for a common outcome the two diverge substantially, with OR overstating the effect relative to RR. See Odds Ratio vs. Risk Ratio for a full side-by-side comparison and How to Interpret an Odds Ratio for the “X times more likely” misreading this distinction most often causes.

Where relative risk is reported

Relative risk is the standard association measure in prospective cohort studies, randomized controlled trials, and cross-sectional prevalence comparisons. It appears throughout clinical epidemiology — drug-safety and efficacy trials, occupational and environmental exposure studies, and public-health surveillance — anywhere a study design permits directly observing incidence in two or more defined groups. A closely related measure for time-to-event data where follow-up time varies between participants is the hazard ratio, produced by Cox proportional-hazards regression rather than a simple risk ratio; see Cox Proportional Hazards Model Explained and How to Interpret a Hazard Ratio.

Frequently asked questions

What is a good relative risk value?

There is no universal “good” threshold — interpretation depends on the outcome’s severity, the exposure’s modifiability, and the absolute risk it’s applied to. An RR of 0.90 (a 10% relative reduction) can be clinically important for a common, severe outcome affecting a large population, while an RR of 0.50 can be nearly meaningless if the underlying absolute risk is vanishingly small. Relative risk should always be reported alongside the absolute risks it was computed from.

Is relative risk the same as relative risk reduction?

No. Relative risk (RR) is the ratio itself. Relative risk reduction (RRR) is 1 − RR, expressed as a percentage reduction — an RR of 0.70 corresponds to an RRR of 30%. Both describe the same underlying comparison in different units; conflating them (reporting an RR value as if it were a percentage reduction) is a common writing error.

Can relative risk be calculated from a case-control study?

Not validly. A case-control study’s case:control ratio is fixed by the researcher rather than reflecting true population incidence, so the cumulative-incidence proportions relative risk requires cannot be recovered from it. Odds ratio is the correct statistic for a case-control design; it approximates relative risk under the rare-disease assumption.