relative risk reduction

Last reviewed 09/2022

• Number Needed to Treat (NNT) is the number of patients who must (on average) be treated with a specific therapy for one of them to benefit
• the NNT is calculated from the proportion of successes (or failures) in those having no treatment, or an alternative treatment. For example, if streptokinase was found to reduce the mortality associated with myocardial infarction from 12% to 8%, then this would mean that for every 100 patients treated with streptokinase 4 (4%) would survive who would otherwise have died. Thus the NNT to save one life with treating with streptokinase is 100/4 = 25. Note that 22, of the other 24 patients who received treatment and survived, would have survived without treatment. Also that 2 patients (8%) died despite the streptokinase treatment.
• trial results used to derive NNTs often considerable uncertainty associated with them but the uncertainty in NNTs is hidden, because they are generally published without confidence intervals

The process of calculating NNT is formalised in the equations below:

Absolute Risk (AR) = ( number of events (good or bad) in treated or control group ) / ( number of people in that group)

ARC = AR of events in the control group

ART = AR of events in the treatment group

Absolute Risk Reduction (ARR) = ARC - ART

Relative Risk (RR) = ART/ARC = 1 - RRR where RRR is Relative Risk reduction

RRR = (ARC -ART)/ARC = 1- RR

NNT = 1/ARR

Notes:

• if there was an increase in risk of events in the treatment group compared to the placebo group then:
  • Absolute Risk Increase (ARI) = ART - ARC
  • Relative Risk Increase (RRI) = ARI / (number of events divided by number of patients receiving active treatment)

Reference:

• Prescribers' Journal (1999), 39 (2), 118-9.