Health Economics Metrics

Topic 46 of 76 · HTA frameworks and prevention economics

Number Needed to Treat (NNT)

NNT is the number of patients who must receive an intervention for one additional patient to benefit, over a stated time frame. It converts percentage risk reductions — which mislead — into effort-per-benefit units that anyone can reason about.

Why it matters

"Reduces heart attacks by 25%!" sounds decisive. If the baseline risk is 4% over 5 years, the absolute reduction is 1 percentage point, so 100 people must take the drug for 5 years for 1 to benefit — and all 100 pay the costs and side effects. NNT is the antidote to relative-risk marketing, which is why evidence-based medicine leads with it. Statins for primary prevention: NNT ≈ 50–100 over 5 years per heart attack avoided. Its mirror, NNH (number needed to harm), counts how many treated per person harmed.

The math

ARR = control event rate − treatment event rate   (absolute risk reduction)
NNT = 1 / ARR

NNH = 1 / (harm rate_treatment − harm rate_control)

Economic bridge:
cost per event prevented = NNT × cost per treatment course

Always state the time frame and baseline population — NNT is meaningless without both.

Worked example

A falls-prediction system in a hospital flags high-risk patients for intervention (bed sensors, review, supervision). Trial: falls with injury drop from 3.2% to 2.4% of admissions.

ARR = 0.8 percentage points → NNT = 1/0.008 = 125
   (125 patients must get the intervention bundle to prevent 1 injurious fall)

Intervention cost ≈ £40/patient → cost per fall prevented = 125 × 40 = £5,000
Cost of an injurious inpatient fall (extra stay, imaging, litigation) ≈ £12,000
Net: prevention pays ~2.4:1 — and the QALY gain is on top.

Note how NNT keeps the claim honest: "reduces falls 25%" and "prevent one fall per 125 patients treated" are the same result, differently persuasive.

Software engineering connection

NNT is the right unit for any gate or check that acts on many items to catch few: "number of PRs that must pass through the AI review gate to catch one production-bound defect." If the gate reviews 400 PRs per real catch (NNT = 400) at 4 minutes of developer attention each, one catch costs ~27 developer-hours — now compare that to the incident cost it prevents. NNH maps to false positives: how many PRs per false flag, and what does each cost in attention and trust? Screening-style tooling (linters, security scanners, anomaly detection) should ship with NNT/NNH arithmetic — see screening economics for why low prevalence makes these numbers brutal.

Pitfalls

  • No time frame: "NNT = 50" means nothing; "NNT = 50 over 5 years" is a claim.
  • Baseline-risk transplantation: NNT computed in a high-risk trial population collapses in a low-risk deployment population.
  • Ignoring NNH — a gate with NNT 400 and NNH 3 is a nuisance generator, not a safety system.

Sources