Confidence intervals for the number needed to treat

The number needed to treat (NNT) is a useful way of reporting the results of randomised controlled trials.1 In a trial comparing a new treatment with a standard one, the number needed to treat is the estimated number of patients who need to be treated with the new treatment rather than the standard treatment for one additional patient to benefit. It can be obtained for any trial that has reported a binary outcome.

Trials with binary end points yield a proportion of patients in each group with the outcome of interest. When the outcome event is an adverse one, the difference between the proportions with the outcome in the new treatment (p_N) and standard treatment (p_S) groups is called the absolute risk reduction (ARR=p_N−p_S). The number needed to treat is simply the reciprocal of the absolute risk difference, or 1/ARR (or 100/ARR if percentages are used rather than proportions). A large treatment effect, in the absolute scale, leads to a small number needed to treat. A treatment that will lead to one saved life for every 10 patients treated is clearly better than a competing treatment that saves one life for every 50 treated. Note that when there is no treatment effect the absolute risk reduction is zero and the number needed to treat is infinite. As we will see below, this causes problems.

As with other …