Missing the point (estimate)? Confidence intervals for the number needed to treat.

T he number needed to treat, that is, the average number of patients a clinician needs to treat with a particular therapy to prevent one bad outcome, 1 is a translation into clinical terms of the absolute risk reduction derived from a trial. Most clinicians are aware that very small absolute risk reductions translate into large numbers needed to treat, which often helps them to distinguish statistically significant from clinically significant results. For example, in a letter in this issue (page 1652), 2 David Gladstone and colleagues use point estimates of the number needed to treat to demonstrate the benefit of tissue plasminogen activator (tPA) in the treatment of stroke. A point estimate represents the single most plausible value in light of the observed data. However the data will generally be consistent with a whole range of values. Along with a point estimate, it is informative to provide a confidence interval reflecting the range of plausible values — and ruling out values outside this range. But the interpretation of confidence intervals for the number needed to treat has some subtleties, and incorrect confidence intervals for the number needed to treat have often been reported. 3 The number needed to treat is computed as the reciprocal of the absolute risk reduction. For example, Glad-stone and colleagues presented the absolute risk reduction for patients with moderate baseline stroke severity (National Institutes of Health Stroke Scale [NIHSS] between 6 and 10) as being 16.6%. The number needed to treat is thus 1/0.166 or approximately 6. This benefit was statistically significant: the 95% confidence interval for the absolute risk reduction was 0.9%–32.2%. A 95% confidence interval for the number needed to treat is 1/0.009 to 1/0.322 or approximately 3.1–111.1 (Note that taking the reciprocal reverses the order of the limits of the confidence interval.) This all seems quite straightforward, that is, until we try the calculation for a nonsignificant result, for example, for patients with low baseline stroke severity (NIHSS score between 0 and 5). The absolute risk reduction was 6.6% with a 95% confidence interval of –20.9% to 34.1%. Naively taking reciprocals gives a number needed to treat of about 15.2 and an apparent 95% confidence interval of –4.8 to 2.9, which does not seem to include 15.2! Clearly some-thing's afoot. To understand the source of the confusion, note first that the lower limit of the confidence interval for the absolute risk reduction …