Probability of adverse events that have not yet occurred: a statistical reminder

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Abstract
The probability of adverse and undesirable events during and after operations that have not yet occurred in a finite number of patients (n) can be estimated with Hanley's simple formula, which gives the upper limit of the 95% confidence interval of the probability of such an event: upper limit of 95% confidence interval=maximum risk=3/n (for n>30). Doctors and surgeons should keep this simple rule in mind when complication rates of zero are reported in the literature and when they have not (yet) experienced a disastrous complication in a procedure. Just as aeroplanes should not crash, common bile ducts should not be cut and iliac vessels not be punctured during laparoscopic procedures. In reality, however, these things do happen.1 With the boom in endoscopic surgery, surgeons are claiming to have zero mortality or even zero morbidity in their series of operations. A little reminder, not only for surgeons, may be necessary. If a certain adverse event or complication does not occur in a series, it does not mean that it will never …