Source of Number needed to treat

{{Infobox concept | name = Number needed to treat | subtitle = Trial methodology | Abbreviation = NNT | Definition = Reciprocal of the absolute risk reduction | Requires = A stated time horizon | Counterpart = Number needed to harm }} The '''number needed to treat''' ('''NNT''') is the number of people who must receive a treatment, rather than the comparator, for one additional person to experience the benefit over a defined period. It is the reciprocal of the absolute risk reduction.{{r|laupacis1988}} Its value is that it expresses effect on an absolute scale. A relative risk reduction of 20% describes a large benefit where the baseline risk is high and a negligible one where it is low; the number needed to treat carries the baseline risk within it.{{r|laupacis1988}} It is meaningless without a time horizon. A treatment with a number needed to treat of 50 over one year and one of 50 over five years are very different propositions, and quoting the figure without the period is the commonest error made with it.{{r|laupacis1988}} == Calculation == {{math|\text{NNT} = 1 / (\text{risk}_{\text{control}} - \text{risk}_{\text{treated}})}} For [[SELECT trial|SELECT]], the primary composite occurred in 8.0% of the placebo group and 6.5% of the semaglutide group over a mean 39.8 months. The absolute risk reduction is 1.5 percentage points, so the number needed to treat is 1/0.015 ≈ 67 over roughly 3.3 years.{{r|lincoff2023}} The corresponding relative figure — a hazard ratio of 0.80, or a 20% relative reduction — is the same result expressed differently and sounds considerably larger. Neither is wrong; they are the same arithmetic.{{r|laupacis1988}} Confidence intervals transfer awkwardly. The interval for a number needed to treat is the reciprocal of the interval for the absolute risk reduction, and it behaves badly when that interval spans zero, which is one reason the measure is best used for statistically significant results.{{r|altman1998}} == Number needed to harm == The same arithmetic applied to an adverse outcome gives the number needed to harm, and the two are only comparable when computed over the same period in the same population.{{r|laupacis1988}} In SELECT, discontinuation for adverse events occurred in 16.6% on semaglutide against 8.2% on placebo — an absolute difference of 8.4 percentage points, giving a number needed to harm of about 12 for that outcome over the same period.{{r|lincoff2023}} Presenting the two side by side is more informative than either alone, and it makes explicit that the outcomes being traded are of different kinds: a cardiovascular event and a discontinuation are not commensurable, and no arithmetic makes them so.{{r|altman1998}} == Limitations == The measure applies to the population studied. Baseline risk drives it, so a number needed to treat computed in an enriched high-risk trial population does not transfer to a lower-risk group; the relative effect transfers more readily than the absolute one.{{r|laupacis1988}} It also assumes a binary outcome. For a continuous endpoint such as weight change, a number needed to treat requires a threshold — for example, the number needed to treat for one additional person to lose 10% of body weight — and the choice of threshold changes the number.{{r|altman1998}} Where the threshold is not pre-specified, the resulting figure is a post hoc construction.{{r|ich_e9}} Finally, it says nothing about the size of the benefit to the person who benefits. Two treatments with identical numbers needed to treat may prevent a transient symptom and a fatal event respectively.{{r|laupacis1988}} == References == {{reflist}} <ref name="laupacis1988">Laupacis A, Sackett DL, Roberts RS. "An assessment of clinically useful measures of the consequences of treatment." ''New England Journal of Medicine'' 318(26):1728–1733 (1988). PMID 3374545.</ref> <ref name="altman1998">Altman DG. "Confidence intervals for the number needed to treat." ''BMJ'' 317(7168):1309–1312 (1998). PMID 9804726.</ref> <ref name="lincoff2023">Lincoff AM, Brown-Frandsen K, Colhoun HM, et al. "Semaglutide and cardiovascular outcomes in obesity without diabetes." ''New England Journal of Medicine'' 389(24):2221–2232 (2023). PMID 37952131.</ref> <ref name="ich_e9">International Council for Harmonisation, ''E9(R1): Estimands and Sensitivity Analysis in Clinical Trials'' (2019).</ref> == See also == * [[Placebo-adjusted effect]] * [[Intention-to-treat analysis]] * [[SELECT trial]] * [[Surrogate endpoint]] * [[Randomised controlled trial]] {{DEFAULTSORT:Number needed to treat}} [[Category:Research methodology]] [[Category:Evidence appraisal]] [[Category:Clinical evidence]]