Relative risk reduction (RRR)
Relative risk reduction (RRR) is the proportional decrease in an outcome's risk in a treated group compared with a control group. It is calculated as (control event rate − experimental event rate) / control event rate, or equivalently 1 − relative risk.
Relative risk reduction (RRR) expresses how much a treatment or exposure lowers the risk of an outcome as a proportion of the baseline risk. The formula is RRR = (control event rate − experimental event rate) / control event rate. Because relative risk (RR) is the experimental rate divided by the control rate, RRR can also be written as RRR = 1 − RR.
Consider a trial where 20% of the control group has a heart attack versus 10% of the treatment group. The RRR is (0.20 − 0.10) / 0.20 = 0.50, a 50% relative risk reduction. The absolute risk reduction (ARR) — simply control rate minus experimental rate — is 0.10, and the number needed to treat (NNT) is 1/ARR = 10 patients.
The distinction between relative and absolute measures matters for interpretation. A 50% RRR sounds dramatic, but if the baseline risk were only 0.2% instead of 20%, the same RRR would correspond to a tiny absolute benefit. RRR is also related to, but distinct from, attributable risk — the risk difference between exposed and unexposed groups, which quantifies how much risk an exposure adds rather than how much a treatment removes.
Measures of association are a reliable biostatistics topic on the USMLE Step 1 exam. Be able to compute RRR, ARR, RR, and NNT from a two-by-two table or event rates, and to recognize when a stem is asking for a relative measure versus an absolute one.
Key takeaways
- RRR = (control event rate − experimental event rate) / control event rate = 1 − relative risk.
- Absolute risk reduction (ARR) is the simple difference in event rates, and NNT = 1/ARR.
- A large RRR can mask a small absolute benefit when baseline risk is low.
- USMLE Step 1 tests calculating RRR, ARR, RR, and NNT from event rates or two-by-two tables.