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How likely is it to go wrong Doctor?

Patients rightly pose difficult questions, and we often wonder too. If you have never seen a horrible complication from a particular drug or intervention how likely is it to happen? A short and illuminating paper from Germany may be very helpful [1] - as the authors say "experience and Murphy's law teach us that catastrophes do happen, and their probability can in fact be calculated by a simple rule of thumb."

The authors use a 1983 paper by a Canadian statistician called Hanley as the basis of their argument - Hanley's original paper was called "If nothing goes wrong is everything alright?". Hanley's formula was that if none of 100 patients exposed had a serious problem which concerned us then we can be 95% confident that the chance of this problem occurring is at most 3 in 100 (3/n).

Eyspasch et al use the information on intraoperative death from vascular injury during laparoscopic appendectomy and cholecystectomy to develop the argument further. No such deaths have been reported in 842 appendectomies and 8192 cholecystectomies. The upper limit of the 95% confidence interval for this disaster (rule of 3) is then about 3/1000 and 3/10000 respectively.

Just because we haven't seen anything terrible happen does not mean that it will not happen. The rule of three allows us to be a little more precise about the chance of it happening.


  1. E Eypasch, R Lefering, CK Kum, H Troidl. Probability of adverse events that have not yet occurred: a statistical reminder. British Medical Journal 1995 311: 619-20.

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