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.Summary points

- The number needed to treat is a useful way of reporting results of randomised clinical trials
- When the difference between the two treatments is not statistically significant, the confidence interval for the number needed to treat is difficult to describe
- Sensible confidence intervals can always be constructed for the number needed to treat
- Confidence intervals should be quoted whenever a number needed to treat value is given

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 estimates, it is important that the uncertainty in the estimated number needed to treat is accompanied by a confidence interval. A confidence interval for the number needed to treat is obtained simply by taking reciprocals of the values defining the confidence interval for the absolute risk reduction.

^{1}^{,2}When the treatment effect is significant at the 5% level, the 95% confidence interval for the absolute risk reduction will not include zero, and thus the 95% confidence interval for the number needed to treat will not include infinity (∞). To take an example, if the ARR is 10% with a 95% confidence interval of 5% to 15%, the NNT is 10 (that is, 100/10) and the 95% confidence interval for the NNT is 6.7 to 20 (that is, 100/15 to 100/5). The case of a treatment effect that is not significant is more difficult. The same finding of ARR=10% with a wider 95% confidence interval for the ARR of −5% to 25% gives a NNT=10 (−20 to 4). There are two difficulties with this confidence interval. Firstly, the number needed to treat can only be positive, and, secondly, the confidence interval does not seem to include the best estimate of 10. To avoid such perplexing results, the number needed to treat is often given without a confidence interval when the treatments are not significantly different.A negative number needed to treat indicates that the treatment has a harmful effect. An NNT=−20 indicates that if 20 patients are treated with the new treatment, one fewer would have a good outcome than if they all received the standard treatment. A negative number needed to treat has been called the number needed to harm (NNH).

^{3}^{,4}As already noted, the number needed to treat is infinity (∞) when the absolute risk reduction is zero, so the confidence interval calculated as −20 to 4 must include ∞. The confidence interval is therefore peculiar, apparently encompassing two disjoint regions—values of the NNT from 4 to ∞ and values of the NNT from −20 to −∞ (or NNH from 20 to ∞), as shown in figure figure1.1. This situation led McQuay and Moore to observe that in the case of a non-significant difference it is not possible to get a useful confidence interval, and so only a point estimate is available.

^{3}It is not satisfactory for the confidence interval to be presented only when the result is significant. Indeed this goes against advice that the confidence interval is especially useful when the result of a trial is not significant.

^{5}In this article I show how a sensible confidence interval can be quoted for any trial. I also consider the use of the number needed to treat in meta-analysis. I approach the problem initially from a graphical perspective.