Letters

Confidence intervals for the number needed to treat

Pooling numbers needed to treat may not be reliable

Absolute risk reduction is less likely to be misunderstood

Pooling numbers needed to treat may not be reliable

EDITORThe 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.

Christopher Cates, General practitioner. 
Manor View Practice, Bushey, Hertfordshire WD2 2NN chriscates{at}emailmsn.com

Absolute risk reduction is less likely to be misunderstood

EDITORAltman describes the number needed to treat as a useful way of reporting the results of randomised controlled trials and proceeds to show how confidence intervals for this measure are calculated.¹ As he shows, however, a confidence interval for an absolute risk reduction from, say, 5% to 25% inverts to a confidence interval that goes from a number needed to treat to benefit of 4, through infinity, to a number needed to treat to harm of 20. My impression from discussing such intervals with clinicians is that they find them difficult to grasp.

Altman correctly argues on general grounds against presenting confidence intervals only for significant effects. Moreover, the potential application in presentations such as forest plots that put together the results of several studies rules out the argument that the number needed to treat should only be estimated when it is significant.

I believe that the number needed to treat has as much potential to confuse as to enlighten. The absolute risk reduction is a more basic quantity, with much less potential to be misunderstood, and should be regarded as the primary measure of effect size. The estimated absolute risk reduction and its confidence interval are most readily grasped when presented in percentages, as in Altman's paper. The number needed to treat and its confidence intervals are better regarded as secondary, whether in the numerical presentation of results or as an additional scale on a diagrama useful informal alternative way of interpreting an absolute risk reduction when it is well away from zero.

Robert G Newcombe, Senior lecturer in medical statistics. 
University of Wales College of Medicine, Cardiff CF4 4XN