A note on the number needed to treat.

The concept of the average number of patients needed to treat to prevent a single bad outcome is becoming increasingly popular among clinicians. Defined as the inverse of the absolute risk reduction (delta), its sample estimate is denoted as NNT. Here we discuss the mathematical and statistical properties of NNT and show that simple calculations, like taking sums of different NNTs, can give nonsensical results. The implication for a meta-analysis expressed in NNTs is that we can best calculate the combined NNT by taking the inverse of the combined estimate for delta. Simulations illustrate the better performance of the combined NNT estimate on the delta-scale (NNT(P)) in comparison with the combined estimate of NNT on the NNT-scale (NNT(O)), even in cases where it is reasonable to take sums. The calculations are illustrated using data from anti-epileptic trials.