Number Needed To Treat - Derivation

Derivation

In general, NNT is computed with respect to two treatments A and B, with A typically the intervention and B the control (e.g., A might be a 5-year treatment with a drug, while B is no treatment). A defined endpoint has to be specified (e.g., the appearance of colon cancer in a five-year period). If the probabilities p_A and p_B of this endpoint under treatments A and B, respectively, are known, then the NNT is computed as 1/(p_B – p_A). NNT is a number between 1 and ∞; effective interventions have a low NNT. A negative number would not be presented as a NNT, rather, as the intervention is harmful, it is expressed as a number needed to harm (NNH). The units of the aforementioned probabilities are expressed as number of events per subject (see worked out example below); therefore, the inverse NNH will be number of subjects (required) per event.