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There are many “rules of three” in medicine, but one in particular stands out in the practice of critical appraisal and evidence based medicine. It’s the rule first described by Handley and Lippmann-Hand in 1983,1 and applies to situations where a study has found no events, or alternatively, everyone has had an event (that is, 0% and 100% outcomes).
This rule of three describes the 95% confidence interval for such a situation. It is calculated by 3/n, where n is the number of subjects studied. (For accuracy, n should be greater than 30.) For example, if you have a trial where 120 children received a new antiemetic, and there were no obvious adverse events, the upper bound of the 95% confidence interval would be 3/120 = 2.5%. You could be fairly sure that no more than about 1 in 40 children would suffer a side effect from this study’s results.
It also works for the other end of the spectrum, where a new therapy (for instance a new antibiotic) has no therapeutic failures in treating impetigo in a trial of 90 children. If 45 received the new antibiotic, then the confidence interval calculated by our rule would be 3/45 = 6.6%; that is, the 95% confidence intervals would be between 93.4% and 100%.
Taking this simple rule to the reading of spectacular results gives the clinician a relatively powerful way of defining what we know instinctively to be true—no news doesn’t necessarily mean good news.
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