Absolute, relative and attributable risk, NNT and NNH

At a glance

• Relative measures (RR, RRR, hazard ratio) tend to stay similar across patients. Absolute measures (ARR, NNT) depend on how likely the patient was to have the event anyway.
• NNT = 1 / ARR, rounded up, with a time frame. NNH = 1 / absolute risk increase.
• The same drug has a small NNT in high-risk patients and a large one in low-risk patients. That is why Australian prevention guidelines treat by absolute risk, not single risk factors.
• Attributable risk asks how much disease an exposure causes, in exposed people and across the whole population.
• Paper 1 gives a trial result and asks for an NNT, or asks why a headline relative risk reduction misleads for a particular patient.

The measures

From a trial, take the control event rate (CER) and experimental event rate (EER) over the same follow-up.

Measure	Formula	Meaning
Relative risk (RR)	EER / CER	Risk on treatment as a fraction of risk on control
Relative risk reduction (RRR)	(CER − EER) / CER = 1 − RR	Proportion of baseline risk removed
Absolute risk reduction (ARR)	CER − EER	Percentage points of risk removed
NNT	1 / ARR	Patients treated for one to benefit
Absolute risk increase (ARI)	Adverse rate on drug − rate on control	Extra harm in percentage points
NNH	1 / ARI	Patients treated for one to be harmed

• RR below 1 means benefit, above 1 means harm. An odds ratio approximates the RR only when the outcome is uncommon (under about 10%).
• Hazard ratios from survival analysis behave like relative risks averaged over follow-up. To get an NNT from an HR you need the control group's absolute risk at a stated time.

Worked example: a lipid-lowering trial

Over 5 years, 10% of patients on placebo and 7.5% on the drug have a major cardiovascular event.

• RR = 7.5 / 10 = 0.75
• RRR = 1 − 0.75 = 25%
• ARR = 10% − 7.5% = 2.5% = 0.025
• NNT = 1 / 0.025 = 40 over 5 years

Now apply the same 25% RRR to a lower-risk patient:

5-year baseline risk	Risk on drug	ARR	NNT (5 years)
20%	15%	5%	20
10%	7.5%	2.5%	40
2%	1.5%	0.5%	200

• A drug company can truthfully advertise a "25% reduction" in all three rows. Only the absolute figures tell a patient what they stand to gain.
• The 2023 Australian guideline uses the Aus CVD Risk Calculator to estimate 5-year risk: high ≥ 10%, intermediate 5% to under 10%, low under 5%. High-risk people get BP-lowering and lipid-lowering therapy together because their NNT is small. See dyslipidaemia and hypertension.

Pitfall: NNTs from trials of different lengths can't be compared directly. An NNT of 40 over 5 years isn't the same as 40 over 1 year. Scaling by time assumes a constant effect, which is often untrue.

Weighing benefit against harm

An anticoagulant cuts annual stroke risk in AF from 4% to 1.5% but raises major bleeding from 1% to 2%.

• ARR = 2.5%, so NNT = 40 per year to prevent one stroke.
• ARI = 1%, so NNH = 100 per year to cause one major bleed.
• About 2.5 strokes are prevented for every major bleed caused. Whether that trade is worth it depends on how the patient values each outcome. Applied to real patients in atrial fibrillation.

Older people have higher baseline risk, so relative benefits often translate into smaller NNTs. Their harms rise too (bleeding, falls, hypotension, drug interactions), and competing causes of death limit time to benefit. Trials often excluded people over 75 with frailty or multimorbidity, so both the NNT and NNH need adjusting to the individual.

Pitfall: benefits reported as relative reductions and harms as absolute increases ("mismatched framing") make drugs look better than they are. Convert both to absolute terms.

Confidence intervals for the NNT

• The CI for the NNT comes from inverting the CI for the ARR.
• ARR 2.5% (95% CI 1% to 4%) gives NNT 40 (95% CI 25 to 100).
• If the ARR CI crosses zero (say −1% to 6%), the NNT CI runs from NNTB 17 through infinity to NNTH 100. Altman's 1998 BMJ paper set out this notation; a single "NNT" figure would hide that the result includes harm. See standard error and confidence intervals and p-values and power.

Attributable risk in populations

Cohort data compare incidence in exposed (Ie) and unexposed (Iu) people.

Measure	Formula	Question answered
Attributable risk (risk difference)	Ie − Iu	Excess disease in exposed people
Attributable fraction (exposed)	(Ie − Iu) / Ie = (RR − 1) / RR	Share of exposed cases due to the exposure
Population attributable risk	Itotal − Iu	Excess disease across the population
Population attributable fraction (PAF)	Pe(RR − 1) / [1 + Pe(RR − 1)]	Share of all cases that removing the exposure would prevent

Worked example: smoking and lung cancer

Suppose lung cancer incidence is 1.5 per 1,000 person-years in smokers and 0.1 per 1,000 in never-smokers, and 12% of adults smoke.

• RR = 1.5 / 0.1 = 15
• Attributable risk = 1.4 per 1,000 person-years
• Attributable fraction in smokers = 14 / 15 ≈ 93%
• PAF = 0.12 × 14 / (1 + 0.12 × 14) = 1.68 / 2.68 ≈ 63%

A strong risk factor that few people have can yield a smaller PAF than a weak one that is common. A modest RR for hypertension, applied to a third of adults, accounts for more cardiovascular disease than a rare monogenic dyslipidaemia with a high RR. This is the basis of population-level prevention, and why burden of disease studies report PAFs.

Pitfall: PAFs for several risk factors often add up to more than 100%, because causes overlap and interact.

How it's tested

• Calculating RR, RRR, ARR and NNT from a 2×2 table or event rates, then applying the RRR to a patient with a different baseline risk.
• Choosing the best explanation for why an NNT in one population differs from another (baseline risk, not drug potency).
• Balancing NNT against NNH for an older patient, often with a geriatric or anticoagulation stem.
• Distinguishing attributable fraction in the exposed from population attributable fraction, and seeing how exposure prevalence changes the PAF.

Pitfalls

• Pitfall: the ARR must be a proportion before inverting. An ARR of 2.5% gives NNT 1 / 0.025 = 40, not 1 / 2.5.
• Pitfall: round the NNT up (39.2 becomes 40). Rounding down overstates benefit. Published trial NNTs are often rounded to the nearest whole number and quoted as "about" (1 / 0.027 = about 37); that is the reporting convention, not an error.
• Pitfall: RRR is often quoted when it is impressive and ARR is small. A 50% RRR from 0.2% to 0.1% gives an NNT of 1,000.
• Pitfall: an NNT from a trial applies to patients like those in the trial, over the trial's duration, with the trial's adherence.
• Pitfall: attributable risk assumes the association is causal and unconfounded. In observational data, confounding can inflate it.