Examples
Worked examples
- Is an instance
A trial of a new anticoagulant for atrial fibrillation follows 1,000 patients per arm for one year. Major bleeding occurs in 50 patients on the anticoagulant (5%) and 20 on placebo (2%). ARI = 5% − 2% = 3 percentage points (0.03). NNH = 1 / 0.03 ≈ 33.3, rounded up to 34 — roughly 34 patients need to take the anticoagulant for one year for one additional patient to have a major bleed that would not otherwise have occurred.
- Is an instance
A post-marketing surveillance study compares a new antibiotic to standard therapy for a specific severe allergic reaction. The reaction occurs in 4 per 1,000 patients on the new antibiotic versus 1 per 1,000 on standard therapy. ARI = 0.4% − 0.1% = 0.3 percentage points (0.003). NNH = 1 / 0.003 ≈ 333.3, rounded up to 334 — about 334 patients need to receive the new antibiotic instead of standard therapy for one additional severe allergic reaction to occur.
Counter-examples
Looks similar, but isn't
- Not an instance
A clinician compares Drug A (NNH = 50 for a mild, self-limiting rash) against Drug B (NNH = 200 for a rare but potentially fatal arrhythmia) and concludes Drug A is 'more harmful' because its NNH is lower. NNH numbers are only directly comparable when the harm being counted is the same severity and the same time horizon — a lower NNH for a trivial, reversible side effect is not automatically worse than a higher NNH for a rare, severe one. Comparing raw NNH values across different outcome types without weighing severity is a common and misleading simplification; NNH must always be read together with what the harm actually is.
Editorial commentary
Number needed to harm (NNH) is the average number of patients who must receive a specific treatment, or be exposed to a specific risk factor, for one additional patient to experience a defined harmful outcome, compared with a control condition, over a stated follow-up period. It is calculated the same way as number needed to treat (NNT) but applied to an adverse event instead of a beneficial one, and the two are used together — not interchangeably — to weigh a treatment’s benefit against its risk.
Formula
NNH = 1 ÷ absolute risk increase (ARI), where ARI = harmful-event rate in the exposed/treated group − harmful-event rate in the unexposed/control group. Because NNH is a reciprocal, it is always rounded up to the next whole number (a fractional patient cannot experience an event), and a higher NNH means the harm is rarer — the opposite direction from how NNT is read, where a lower number is better. This inverted reading is the single most common source of confusion when NNT and NNH are reported side by side.
Worked example
A trial of a new anticoagulant for atrial fibrillation follows 1,000 patients per arm for one year.
| Major bleed | No major bleed | Total | |
|---|---|---|---|
| Anticoagulant | 50 | 950 | 1,000 |
| Placebo | 20 | 980 | 1,000 |
Rate(anticoagulant) = 50/1,000 = 5%. Rate(placebo) = 20/1,000 = 2%. ARI = 5% − 2% = 3 percentage points (0.03). NNH = 1 / 0.03 ≈ 33.3, rounded up to 34. Roughly 34 patients need to take the anticoagulant for one year for one additional major bleed to occur that would not otherwise have happened. This NNH is only meaningful alongside the trial’s NNT for the drug’s intended benefit (stroke prevention) — see the worked NNT example in Absolute Risk Reduction, Relative Risk Reduction, and Number Needed to Treat.
Weighing NNH against NNT
A treatment’s overall risk-benefit profile is not read from NNT or NNH alone but from the relationship between them, for the same population and time horizon:
| What it measures | Better direction | |
|---|---|---|
| NNT | Patients treated per one additional patient benefiting | Lower is better |
| NNH | Patients treated per one additional patient harmed | Higher is better |
A treatment with NNT = 20 for its primary benefit and NNH = 200 for a serious adverse event is, all else equal, a considerably more favourable trade-off than one with NNT = 20 and NNH = 25 — in the second case, roughly as many patients are harmed as benefit. Comparing NNT and NNH is only valid when both are measured over the same time horizon and both outcomes are weighed for actual severity, not treated as interchangeable “one number is better” comparisons; see the counter-example below for how that comparison goes wrong. Evidence-based-medicine teaching sometimes formalizes this trade-off as the likelihood of being helped versus harmed (LHH), the ratio NNH ÷ NNT: a large LHH (harm much rarer than benefit) favors treatment, a small or sub-1 LHH does not — though the benefit and harm being compared are rarely of equal clinical severity, which is why LHH is a starting heuristic rather than a decision rule on its own.
Where NNH is reported
NNH appears in randomized trial safety reporting, pharmacovigilance and post-marketing surveillance analyses, and shared decision-making tools that present a treatment’s benefits and harms side by side for patients and clinicians. Number needed to treat was introduced by Laupacis, Sackett, and Roberts in 1988 as a way to express a trial’s benefit in a single clinically intuitive number rather than a relative measure alone; NNH extended that same framework to adverse outcomes shortly after. Both numbers depend entirely on the population and time horizon they were measured in and do not transfer automatically to a different population with a different baseline risk. Where a trial or systematic review reports NNH for a pre-specified safety outcome, the accompanying CONSORT-guided results section should state the absolute event rates in both arms, the ARI with its confidence interval, and the follow-up duration the NNH was calculated over, so a reader can see both numbers were derived the same way and can be compared directly.
Limitations
- Requires a statistically significant ARI. When a trial’s risk difference is not statistically significant, the resulting NNH is not a stable, meaningful number — report the risk difference and its confidence interval instead of a single NNH.
- Time-horizon dependent. The same ARI over 30 days versus 5 years produces a materially different underlying event-accrual rate even though the NNH arithmetic looks identical; always report NNH alongside the outcome definition and follow-up duration.
- Not transportable across populations. NNH calculated in a low-baseline-risk trial population will not predict the same number in a higher-risk population, because ARI (an absolute measure) scales with baseline risk in ways a relative measure does not.
Frequently asked questions
What does a higher NNH mean?
A higher NNH means the harm is rarer — more patients would need to be exposed for one additional harmful event to occur. This is the opposite of NNT, where a lower number indicates a stronger, more easily achieved benefit; the inverted reading is the most common source of confusion when the two are reported together.
Is NNT the same as NNH?
No. NNT quantifies how many patients must be treated for one to benefit; NNH quantifies how many must be treated (or exposed) for one to be harmed. They use the identical reciprocal-of-a-risk-difference arithmetic but are calculated from opposite outcome types, and a treatment’s risk-benefit profile is judged by comparing the two together, not by either number alone.
Can NNH be negative or infinite?
NNH is undefined (approaches infinity) when the absolute risk increase is exactly zero — no difference in harm rate between groups. If the treatment group actually has a lower harm rate than control (a negative ARI), the reciprocal produces what is sometimes reported as an NNT for that “harm” instead, since the treatment is protective against it rather than causing it; this reversal is a sign to re-check which group has the higher event rate before reporting either number.
Can NNH be calculated from a hazard ratio instead of raw event rates?
Not directly with a single conversion factor — a hazard ratio describes relative instantaneous risk over time, while NNH requires an absolute risk increase at a specific follow-up duration. Converting requires the control-arm baseline event rate at that duration, then applying the hazard ratio to derive the treated-arm rate before subtracting to get ARI; a bare hazard ratio alone is not sufficient.
Also known as
NNH
Machine-readable encodings
Use in your systems
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