When should an effective treatment be used? Derivation of the threshold number needed to treat and the minimum event rate for treatment.

Clinicians and patients must decide when treatment effects are large enough to more than offset the adverse effects and costs of therapy. Calculation of the number of patients one needs to treat (NNT) in order to prevent one patient from having the target event is one tool to help with this decision. Clinicians should treat patients when the NNT is lower than a threshold NNT at which point the therapeutic risk equals the therapeutic benefit. We aimed: (1) to identify the determinants of the threshold NNT, and (2) to derive equations for the explicit estimation of the threshold NNT and of the minimum expected rate of target event, without treatment, above which treatment is justified. We conceived the threshold number needed to treat to prevent one target event as the point at which the benefits of treating that number of patients equal the negative consequences of treating that same number of patients. After identifying the various elements comprising the treatment impact, we equated the benefits and negative consequences and solved the equation for threshold NNT. We then derived the minimum expected rate of target event which would justify treatment. We derived an equation that relates the threshold NNT to the treatment-attributable adverse event rates (AER) and the relative values (RV) of the adverse events compared to that of the target event prevented. Specifically, the threshold NNT, denoted NNT(T) is given by NNT(T) = 1/(AER(1).RV(1) +...+ AER(n).RV(n)). We also derived a more complex equation which addresses the costs incurred by treatment and costs avoided by preventing target events. Solving the equation that includes costs requires specifying both the value of preventing a target event and the values of adverse treatment effects in economic units. The threshold NNT and the relative risk reduction (RRR) for the target event determine the minimum target event rate above which treatment is justified. This minimum event rate for treatment is 1/(NNT(T).RRR). The values that clinicians and patients use determine the threshold NNT and therefore also the minimum target event rate, without treatment, above which treatment is justified. Quantification of the determinants of the threshold NNT and of the minimum event rate to justify treatment can assist clinicians and patients in the explicit use of underlying values when making treatment decisions.