Confidence intervals for the number needed to treat

Editor—The number needed to treat has become a popular summary statistic for the results of randomised controlled trials because it combines the treatment effect with the background level of risk in the population studied. Patients in a single trial are randomised for both of these factors, and a confidence interval can be calculated which estimates the statistical uncertainty of the number needed to treat in this particular population.1 Problems arise when comparisons are made between numbers needed to treat from different randomised trials, or when the numbers needed to treat from several trials are combined in a meta-analysis. Often the background level of risk varies between trials in a non-random fashion, depending on the entry criteria in each trial. If the relative benefit of the treatment is constant across these background levels of risk then the number needed to treat in each trial will decrease as the severity of the condition of patients included in the trial rises. Pooling numbers needed to treat may not give a reliable answer in these circumstances, as the entry criteria of each trial will confound the treatment effect. The meaning of a confidence interval around a pooled number needed to treat poses difficulties when the background level of risk among trials varies widely. I would therefore support Egger et al’s suggestion that the pooled results of meta-analyses are reported in terms of a summary statistic which describes the relative benefit of a treatment (such as relative risk).2 If the pooled relative risk is reported with its confidence interval both can be applied to any chosen control group event rate. In figure 3 in Altman’s paper the pooled relative risk is 0.62 (95% confidence interval 0.52 to 0.74). When the background rate of angina in the group given percutaneous transluminal coronary angioplasty is 28% (such as found in the German angioplasty bypass surgery investigation (GABI), which included patients with more severe angina) the number needed to treat for coronary artery bypass grafting would be 8.67 (6.87 to 12.67). If the background rate of angina in the percutaneous transluminal coronary angioplasty group is lower (such as the 16% found in the coronary angioplasty versus bypass revascularisation investigation (CABRI)) then the number needed to treat would be 16.85 (13.34 to 24.63). Finally, I would suggest that numbers needed to treat are always accompanied by the control group event rate to which they apply and the relative risk and confidence interval from which they are derived.