Improving the calculation of confidence intervals for the number needed to treat

The number needed to treat has gained much attention in the past years as a useful way of reporting the results of randomised controlled trials with a binary outcome. Defined as reciprocal of the absolute risk reduction the number needed to treat is the estimated number of patients who need to be treated to prevent an adverse outcome in one additional patient. As with other estimated effect measures, it is important to document the uncertainty of the estimation by means of an appropriate confidence interval. Confidence intervals for the number needed to treat can be obtained by inverting and exchanging the confidence limits for the absolute risk reduction. Unfortunately, the only method used in practice for calculating a confidence interval for the absolute risk reduction seems to be the usual asymptotic method, which yields confidence intervals which are too short in many cases. In this paper it is shown that the application of the Wilson score method improves the calculation and presentation of confidence intervals for the number needed to treat.