Bug Fixed: lower bound of 95% confidence interval for Attributable risk (difference between proportions) reported incorrectly in Prism 9.2.0

The issue

When performing the analysis “Chi-square (and Fisher’s exact) test”, one of the effect sizes that Prism can report is the difference between proportions (attributable risk) and NNT (the number needed to treat). When this option is selected, Prism will also report the 95% confidence interval for this effect size. In Prism 9.2.0, if the lower limit of this confidence interval was negative, Prism would incorrectly report the lower bound of the CI as zero (see screenshots below). This issue was only present in Prism 9.2.0 (it was absent in earlier versions and has been fixed in 9.3.0).

Prism 9.2.0 results (incorrect)

Results in Prism 9.3.0 (and prior to 9.2.0)

Calculating the lower bound manually

It is possible to manually calculate a correct lower bound using the results that Prism 9.2.0 reports and the simple asymptotic method. To do so, use the following simple formulas:
Error = Upper_Bound - Attributable_Risk_Value
Lower_Bound = Attributable_Risk_Value - Error

In the example above, this corresponds to:
Error = 0.04236 - 0.006230 = 0.03613
Lower_Bound = 0.006230 - 0.03613 = -0.0299

This value is close to what is reported in Prism 9.3.0 for the lower bound. Please be aware, however, that by default Prism uses the Newcombe/Wilson score method with continuity correction to calculate the 95% confidence interval. The calculations required for this method are a bit more complicated and are not shown here. Thus the confidence limits calculated manually using the method above may not perfectly match the results that Prism generates (unless the Simple asymptotic method was selected in the analysis parameters options).

Confidence interval of NNT

Note that as a result of this correction to the way the 95% CI for Attributable risk is reported, the 95% CI for NNT may also be updated. When the 95% CI for attributable risk contains zero, it is not possible to report the 95% CI for NNT (which is the inverse of attributable risk). Thus, in these cases, the 95% CI for NNT is simply reported as blank.

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