Absolute & Relative Risk Reduction (ARR & RRR)
The two ways to express a treatment’s benefit — one tells the real-world story, the other inflates it.
ARR is the absolute difference in event rates: ARR = CER − EER. RRR is the proportion of the baseline risk removed: RRR = ARR ÷ CER = (CER − EER) ÷ CER. The ARR is what determines the NNT: NNT = 1 ÷ ARR.
CER 16/100 → RRR ≈ 9% of baseline removed, but ARR ≈ 1.5% · NNT = 1 ÷ ARR ≈ 67
16 of the 100 placebo figures are highlighted — the baseline risk. Treatment removes only a sliver of that crowd: about 1.5 figures in 100 (the ARR). Expressed as a fraction of the 16, that sliver is ~9% (the RRR). Same effect, two very different-sounding numbers.
RRR answers “what fraction of the baseline risk did we remove?” — it stays roughly constant whatever the baseline. ARR answers “how many extra people per 100 benefit here?” — and it shrinks as the baseline risk falls. The ARR, not the RRR, is what converts into an NNT and a real-world decision.
RRR is the number that sells the drug; ARR is the number that decides whether to use it. A constant 30% RRR sounds the same in everyone, but at a 20% baseline it means ARR 6% (NNT 17), and at a 1% baseline it means ARR 0.3% (NNT 333). Demanding the ARR is the single fastest defence against relative-risk hype.
ARR = CER − EER·RRR = ARR ÷ CERNNT = 1 ÷ ARR— only the absolute figure gives an NNT- RRR is ~constant across baselines; ARR shrinks as baseline risk falls
CRASH-2 (Lancet 2010) — 20,211 bleeding trauma patients, tranexamic acid vs placebo. 28-day mortality CER 16.0% (1613/10060), EER 14.5% (1463/10067). So RRR ≈ 9% (1 − 0.91), but ARR ≈ 1.5% and NNT ≈ 67. The relative figure sounds modest; the absolute figure is what justified rolling TXA into trauma protocols. The pooled ARR averages over time-to-treatment: benefit concentrates in patients treated ≤3 h, while >3 h the subgroup had more bleeding deaths — so a single ARR can mask important subgroup variation.
- RRR quoted without ARR — the classic way a marginal benefit is dressed up as a big one.
- Forgetting ARR depends on baseline risk — the same RRR gives a smaller ARR (and larger NNT) in low-risk patients.
- Relative-framing bias — people (and exams) rate a treatment more favourably when the same effect is shown as RRR rather than ARR.
Quick check
A drug has a 25% relative risk reduction — how many patients benefit?
Answer: You can’t say. RRR is a proportion of the baseline risk, so you need the control event rate to get ARR (= RRR × CER) and then NNT (= 1 ÷ ARR). At CER 20% that’s ARR 5%, NNT 20; at CER 1% it’s ARR 0.25%, NNT 400.
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