A Note on the Number Needed to Treat
Introduction
Classical measures to express the gain of a treatment in comparison with a control treatment are the absolute risk reduction (Δ), the risk ratio, and the odds ratio. Recently, Cook and Sackett discussed using instead 1/Δ, the (population) average number of patients needed to treat to prevent a single bad outcome [1]. The point estimate of 1/Δ, called the number needed to treat, is denoted as NNT. This measure is becoming popular among clinicians, who perceive it as clinically more relevant than a risk ratio or an odds ratio. As an example we shall consider meta-analyses of anti-epileptic trials. Elferinck and Van Zwieten-Boot [2] questioned the appropriateness of a meta-analysis performed by Marson, Kadir, and Chadwick [3] for clinicians because the summary statistic used was the odds ratio. Elferinck and Van Zwieten-Boot claimed to obtain clearer results when they based the meta-analysis on the NNT.
In Section 2 we illustrate the NNT measure with a clinical trial in epilepsy. In Section 3, we investigate the mathematical and statistical properties of the NNT. In Section 4 we consider the use of confidence intervals. We discuss and illustrate in Section 5 the use of NNT in meta-analyses, and we close with Section 6.
Section snippets
The nnt illustrated in an anti-epileptic drug trial
A double-blind, placebo-controlled study in Europe has assessed in 47 patients the efficacy and safety of topiramate 400 mg/day as adjunctive therapy to traditional anti-epileptic drugs for partial onset seizures with or without secondary generalization [4]. Patients enrolled had seizure rates of at least one seizure per week during an 8-week baseline period. They were randomly assigned to topiramate treatment (n = 23) or placebo (n = 24) for a three-week titration period followed by an
Scale of the NNT
Suppose π1 and π0 are the proportions of responders for the active and control treatment, respectively. Further, let p1 (p0) be the sample estimates of π1 (π0) and Δ̂ = p1 − p0 be the sample estimate of the population absolute risk reduction Δ = π1 − π0. The NNT, or 1/Δ̂, serves as an estimate for 1/Δ.
The NNT is simple to calculate and interpret. Whenever we employ a statistic we should consider its mathematical and statistical (bias and variance) properties. Because the NNT is the inverse of
Reporting confidence intervals
If we use the asymptotic normal distribution of Δ̂, the 95% confidence interval (CI) for 1/Δ is approximately equal to [1/(Δ̂ + 1.96·SE(Δ̂)), 1/(Δ̂ − 1.96·SE(Δ̂))], but only when we invoke the reciprocal transformation in a region where it is continuous. For instance, in the topiramate study, the 95% CI of the NNT equals [2.01, 24.6], which is quite wide and reflects the relatively small sample size of the study. If the 95% CI for Δ encloses 0, however, then the 95% CI for 1/Δ is actually a
Use of the nnt in meta-analyses
In a meta-analysis, we need to combine the NNTs of the individual studies. The combined absolute risk reduction, Δ̂P, with weights as given by Hedges and Olkin [6], is an unbiased estimate of Δ (see also Appendix). When based on a large number of cases, it is also very precise. Therefore, the inverse of Δ̂P, NNTP, will be a fairly unbiased estimate of 1/Δ. We now show this with a limited simulation study. For purely comparative reasons we also consider NNTO, the combined estimate on the NNT
Closing remarks
Although the NNT is a simple and valuable tool for individual trials as well as for meta-analyses, we show that it has undesirable statistical properties. From our calculations above we infer the following.
When investigators use the NNT for reporting the outcome of a single trial, the operational characteristics of the NNT distribution depend on the way it is employed. As a secondary statistic, that is, as a tool for conveying a message for a significant trial on the basis of the absolute risk
Acknowledgements
We thank the editor and two anonymous referees for their positive criticism. Their remarks helped to improve both the content and the organization of this paper.
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