Number Needed to Treat and the Limits of Significance | AI Learning Guide

The number needed to treat is just one divided by the absolute risk reduction, so it inherits everything you saw on the first page: the same relative effect gives a small NNT at high baseline risk and a large NNT at low baseline risk. Now look at the two columns. On the left, a very large trial finds a statistically significant benefit for a rare event, with an NNT of five hundred. The result is real, but treating five hundred patients to prevent one event may not be worth the harms, cost, and burden, and that judgment is clinical, not statistical. On the right, a small trial finds an NNT of five, which sounds impressive, but the confidence interval crosses the null, so the study was simply underpowered. In both columns the p-value and the clinical judgment point in different directions, and the NNT is what makes that tension visible.

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The number needed to treat is the reciprocal of the absolute risk reduction: \[\text{NNT} = \frac{1}{\text{ARR}}\] where ARR is the absolute difference in event risk between the control and treated groups, expressed as a proportion. A baseline risk of 20% reduced to 10% gives \(\text{ARR} = 0.10\) and \(\text{NNT} = 10\). The same relative reduction applied to a baseline risk of 2% gives \(\text{ARR} = 0.01\) and \(\text{NNT} = 100\).

Statistical significance and clinical significance can disagree

Statistically significant, clinically trivial

Very large sample detects a small effect
NNT of 500 for a rare event
p < 0.05 but the benefit may not justify harms, cost, or burden

Clinically important, not statistically significant

Small sample lacks precision
NNT of 5 but the confidence interval crosses the null
The honest conclusion is that the study was underpowered

The number needed to treat is itself an estimate with a confidence interval. A single NNT value reported without its interval can make an uncertain effect look more definite than it is.