If Almost Nothing Goes Wrong, Is Almost Everything All Right? Interpreting Small Numerators

Thomas B. Newman, MD, MPH
JAMA. 1995;274(13):1013. doi:10.1001/jama.1995.03530130019013.
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To the Editor.  —Twelve years ago in an article entitled "IfNothing Goes Wrong, Is Everything All Right?" Drs Hanley and Lippman-Hand1 provided a helpful rule of thumb for interpreting numerators of 0. They showed that if 0 events are observed in N trials, the upper limit of the 95% confidence interval (CI) for the frequency of events is approximately 3/N. Thus, if there are no deaths among 50 patients treated with a new medication, the upper limit of the 95% CI for the risk of death is about 3/50, or 6%. On the other hand, if no deaths occur in a study of 1000 patients, the upper limit of the 95% CI for the mortality rate is 3/1000, or 0.3%.I have found that similar approximations work for other small numerators and that they can be a helpful shortcut when scanning journal articles. In each case, as the denominator


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