Revision aid, not clinical advice. This page is educational material written for exam preparation. It is not a substitute for the current guideline or for clinical judgement, and must not be relied on for the care of any individual. Always check up-to-date national guidance and verify independently before acting on anything here.

AKT Statistics Guide · Part 4 · Chapter 12

Risk & Reward: ARR, RRR & NNT

Why a “50% reduction” can be almost nothing — and the three numbers that tell your patient what a treatment is really worth.

▶Watch the tutorial · 6 min — relative vs absolute risk and NNT, with the worked numbers on screen.

Where this shows up in the AKT

Interpreting a trial result and a quoted drug benefit.
Counselling a patient on whether a treatment is worth taking.
Calculating ARR and NNT from two event rates.
The classic relative-versus-absolute trap — the single most tested idea here.

Drug companies love a dramatic-sounding relative risk reduction. Clinicians need the more honest measures — the absolute risk reduction and the number needed to treat. The AKT tests whether you can see through the marketing spin.

Three definitions

Absolute risk reduction (ARR)

ARR = control risk − treatment risk — the real, actual difference the treatment makes. It is a difference, measured in percentage points.

Relative risk reduction (RRR)

RRR = ARR / control risk — the proportion of the starting risk that is removed. It is a ratio, and it says nothing about how risky the patient was to begin with.

Number needed to treat (NNT)

NNT = 1 / ARR (when ARR is a decimal), or equivalently NNT = 100 / ARR when ARR is in percentage points.
It answers: “How many patients must I treat to prevent one event?” A lower NNT is a more impressive treatment. Round up to the next whole patient if it does not divide neatly.

Worked example

In a trial, 20 in 100 control-group patients have the event (a risk of 20%). On treatment, it is 10 in 100 (a risk of 10%). One trial, three very different-sounding numbers:

Control risk 20%, treatment risk 10%. The same trial, three measures.
Measure	Calculation	Result
ARR	20% − 10%	10 percentage points
RRR	0.10 / 0.20	50%
NNT	1 / 0.10	10

The ARR is 10 percentage points — the actual drop in risk.
The RRR is 50% — which sounds enormous, and is the figure an advert would headline.
The NNT is 10 — treat ten patients to prevent one event.

The trap: baseline risk is everything

Now take that same 50% relative risk reduction, but apply it to a low-risk patient whose baseline risk is only 2%, falling to 1%. The relative reduction is still a glorious 50% — but watch the absolute numbers:

Identical 50% RRR, very different real-world benefit.
Baseline risk	Treated risk	RRR	ARR	NNT
20% (high)	10%	50%	10%	10
2% (low)	1%	50%	1%	100

Same headline, but ten times as many patients to help one person. The relative risk reduction hides the baseline; the ARR and NNT are the numbers that tell the patient what they will actually gain. The riskier the patient, the bigger the absolute benefit from the very same drug — which is exactly why we target treatment at higher-risk people, and why adverts love a relative figure while honest consent needs the absolute one.

Pearl — relative sells, absolute helps. RRR is the marketing number; ARR and NNT are the consultation numbers. When a benefit is quoted only as a percentage reduction, ask what the baseline risk was before you believe it.

Same 50% RRR, different ARR and NNT by baseline risk

Identical 50% relative risk reduction, two very different patients: the high-risk patient gains an ARR of 10% (NNT 10); the low-risk patient just 1% (NNT 100).

The traps that cost marks

Trap 1 — quoting RRR as the real benefit. A 50% reduction from 0.2% to 0.1% is tiny in absolute terms. A large RRR does not mean a large clinical effect.

Trap 2 — the NNT calculation slips. NNT = 100 / ARR (in %). An ARR of 2% gives NNT = 50, not 100. Mixing up ARR (a difference) with RRR (a ratio) is the commonest error.

Trap 3 — treating ARR and NNT as fixed properties of a drug. They are not. They vary with baseline risk (higher baseline risk → lower NNT → bigger benefit) and with the time period over which the risk is measured.

AKT-style question

A statin reduces the risk of cardiovascular events from 4% to 2% over 5 years. The manufacturer advertises this as a “50% reduction in risk”. Which statement best describes this claim?

It is accurate and reflects the absolute risk reduction
It is misleading because it uses the relative risk reduction
It is incorrect because the NNT is 2
It is incorrect because the absolute risk reduction is 50%

Reveal answer

B — it uses the relative risk reduction. The risk drops from 4% to 2%, an absolute risk reduction of just 2 percentage points (NNT = 100 / 2 = 50). The quoted 50% is the relative risk reduction, which often sounds dramatic but exaggerates a small effect. ARR and NNT give the realistic picture a patient needs for consent.

Lock it in

ARR = control risk − treatment risk (a difference).
RRR = ARR / control risk (a ratio) — it hides the baseline.
NNT = 1 / ARR (or 100 / ARR in %) — lower is better.
The same RRR can mean wildly different NNTs depending on baseline risk: relative sells, absolute helps.

Source concepts: standard evidence-based-medicine methodology (e.g. Centre for Evidence-Based Medicine; NICE guidance on communicating risk). A revision summary, not a clinical protocol.

Want more questions like this one?

Try the free 20-question AKT taster: sixteen clinical, two evidence-based practice and two admin questions, with the reasoning after each and a marked report. No card needed. The full AKT Pack has 2,000+ more.

Note: Independent revision resource for the MRCGP AKT and the MSRA. Educational content for exam preparation only — not clinical advice, and not affiliated with the RCGP. A study aid, not a substitute for the official curriculum or clinical judgement.

← Back to the AKT Statistics Guide

by Core Revision · corerevision.com