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AKT Statistics Guide · Part 4 · Chapter 13

Number Needed to Harm

The mirror image of the NNT — counting the patients a treatment might harm, so you can weigh benefit against risk.

▶Watch the tutorial · 6 min — calculating NNH and reading it alongside the NNT.

Where this shows up in the AKT

  • Weighing a drug’s benefit against its side effects.
  • Shared decision-making and informed consent.
  • Calculating NNH from adverse-event rates.
  • Comparing NNT and NNH for the same treatment.

Last chapter we counted the patients we help with the number needed to treat. The number needed to harm counts the ones we might hurt. Its real power is sitting right next to the NNT — put the two side by side and you can actually judge whether a treatment is worth it.

The definition

The maths mirrors the NNT exactly — it is the same calculation, just pointed at a bad outcome instead of a good one.

Absolute risk increase (ARI)

  • ARI = harm rate on treatment − harm rate on control — the extra harm caused by the treatment.

Number needed to harm (NNH)

  • NNH = 1 / ARI (or 100 / ARI when ARI is in percentage points) — how many patients you would treat for one extra person to be harmed.
Pearl — bigger NNH = safer. A large NNH means the harm is rare, so you would have to treat many people before causing one. A small NNH means the harm is common. This is the opposite of the NNT, where small is good.

Worked example

A side effect occurs in 6% of treated patients and in 1% of those on placebo. So the absolute risk increase is 6% − 1% = 5 percentage points (0.05).

Harm rate 6% on treatment vs 1% on placebo.
MeasureCalculationResult
ARI6% − 1%5 percentage points
NNH1 / 0.0520

So the NNH is 20: treat twenty patients and, on average, one extra person suffers that side effect because of the drug.

Reading NNT and NNH together

  • Low NNT + high NNH = plenty of benefit, rare harm — the dream.
  • High NNT + low NNH = little benefit, frequent harm — a poor bargain.
  • Always compare the seriousness of the events, not just the bare numbers.
  • A mild, reversible side effect at an NNH of 20 may be perfectly acceptable; a fatal one at the same NNH would not be.

Picture one drug with both numbers — an NNT of 10 for benefit and an NNH of 100 for a given side effect. For every ten you treat you prevent an event, while you would need a hundred to cause that harm, so the benefit is about ten times more common. A reassuring shape — but the final call still rests on severity, context, and what matters to the patient in front of you.

Pearl — the worthwhile test. A treatment is generally only worthwhile if the NNT is meaningfully lower than the NNH for the harm you are worried about. That comparison, weighted by how serious each outcome is, is the heart of shared decision-making.

The traps that cost marks

Trap 1 — thinking a small NNH is good. It is the opposite. Small means the harm is common, so a small NNH is bad. Big NNH = rarer harm = safer.
Trap 2 — comparing NNT and NNH on the numbers alone. An NNH of 50 for a rash is not the same as an NNH of 50 for a fatal bleed. Always weigh the severity of each event.
Trap 3 — forgetting the time period. Like the NNT, the NNH depends on how long the study followed patients. The two numbers are only comparable over the same time frame.
AKT-style question

A new anticoagulant prevents stroke in 4% of patients over 5 years (ARR 4%) but causes major bleeding in 1% who would not otherwise have bled (ARI 1%). Which statement best describes the trade-off?

  • Unfavourable — the NNH of 25 is lower than the NNT of 100
  • Favourable — the NNT of 25 is lower than the NNH of 100
  • The two exactly cancel out, so the drug has no net effect
  • The NNH is irrelevant once an ARR is known
Reveal answer

B — favourable. NNT = 100 / 4 = 25 (treat 25 to prevent one stroke); NNH = 100 / 1 = 100 (treat 100 to cause one major bleed). The benefit occurs about four times as often as this harm, so the NNT being well below the NNH points to a favourable trade-off — though the seriousness of a major bleed and the patient’s own priorities still finish the conversation.

Lock it in

  • ARI = harm rate on treatment − harm rate on control.
  • NNH = 1 / ARI (or 100 / ARI in %).
  • Bigger NNH = safer, because the harm is rarer.
  • Judge a treatment by setting the NNT against the NNH — and always weigh how serious each outcome is.
Source concepts: standard evidence-based-medicine methodology (e.g. Centre for Evidence-Based Medicine; NICE guidance on communicating benefits and harms). A revision summary, not a clinical protocol.

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