Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 41 / 1 / g / Solution

The number needed to treat is the reciprocal of the absolute reduction in the 12-week adverse-outcome risk. Using the counts rather than rounding the percentages first givesThis means about nine high-risk women would need to be offered the intervention to prevent one additional screen-defined case over that follow-up, under the trial's comparison. It is not a lifetime quantity or automatically an estimate for clinical-interview diagnoses. Calculating from the rounded difference $25\%-14\%$ gives approximately nine but need not give the same integer rounding; the exact counts explain the reported value.

For a confidence interval, first construct an interval for the difference between the two independent event proportions, allowing for binomial distribution sampling uncertainty. If both risk-reduction endpoints are positive, take their reciprocals and reverse their order to obtain an NNT interval. A bootstrap can instead resample women within their randomized controlled trial arms and transform the resulting risk-difference distribution. If the difference interval includes zero, the NNT confidence set extends through infinity and can include harm as well as benefit; it is not an ordinary bounded interval. The raw-outcome interval also relies on the missing-outcome assumptions discussed above.