Relative Risk

The risk of the outcome in the exposed/treated group divided by the risk in the control group: RR = EER ÷ CER. RR < 1 = risk reduced, RR > 1 = risk increased, RR = 1 = no effect. It is a purely relative measure — it ignores how big the baseline risk was.

The top two rows are the placebo arm (16 of 100 died); the bottom two are the treated arm (~14–15 of 100 died). RR compares the two as a ratio: 0.91 means the treated group’s risk is 91% of the control group’s — a 9% relative reduction. Notice the actual gap between the highlighted crowds is tiny.

Read RR as “risk in my group is X times the comparator’s.” Subtract from 1 for the relative risk reduction (1 − 0.91 = 9%). Crucially, the same RR can sit on a huge or a trivial absolute gap depending on the baseline risk — so always ask what the control event rate was before being impressed.

Because RR is roughly constant across baseline risks, a drug can show the same headline RR in a high-risk and a low-risk population — yet the absolute benefit collapses as baseline risk falls. A “33% reduction” (RR 0.67) is dramatic when 30% die and almost meaningless when 0.3% do. RR alone cannot tell you which.

• RR = EER ÷ CER · RRR = 1 − RR
• RR < 1 protective · = 1 no effect · > 1 harmful
• Relative measure — always pair it with the absolute risk/ARR

CRASH-2 (Lancet 2010) — 20,211 bleeding trauma patients, tranexamic acid vs placebo. 28-day all-cause mortality 14.5% (1463/10067) vs 16.0% (1613/10060): RR 0.91 (95% CI 0.85–0.97), p=0.0035. A statistically solid 9% relative reduction — but the absolute gap is only ~1.5%, giving an NNT of ~67. The relative effect is real, yet time-critical: TXA given ≤3 h reduces death, whereas >3 h the subgroup had more bleeding deaths — one pooled RR hides that interaction.

• Relative vs absolute — a large RRR can mask a trivial ARR when baseline risk is low; never judge a trial on RR alone.
• RR vs OR — they are not interchangeable; the odds ratio exaggerates (sits further from 1) when the outcome is common.
• Direction — RR < 1 is protective and RR > 1 is harmful; misreading the side of 1 inverts the clinical message.