= 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 gives
$$
\widehat\Delta=\frac{78}{316}-\frac{40}{297}\simeq0.11216,
\qquad\boxed{\mathrm{NNT}=\frac1{\widehat\Delta}\simeq8.92,\ \text{reported as }9.}
$$
This 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.
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