Bayes' theorem: a negative example of a RCT on grommets in children with glue ear

Bayesian inference presupposes that practitioners' belief in the effectiveness of medical intervention is the product of prior belief and recent evidence from studies. Although increasingly used, up to now the posterior belief calculated according to the theorem has not been compared with an empirically measured posterior belief. We conducted a RCT, which was preceded by elicitation of prior beliefs among ENT-surgeons, and which was followed by elicitation of posterior beliefs among ENT-surgeons, 1 year after completion of the trial. We compared the posterior beliefs of ENT-surgeons about the effect of grommets in children with glue ears, as predicted by Bayes' theorem with actual measured posterior beliefs. The distribution of the measured posterior beliefs was not in line with the calculated posterior, but almost identical to the distribution of the measured prior beliefs. The results showed that our trial had little or no impact on the beliefs of the ENT-surgeons, i.e. they did not adjust their belief to the extent that was expected according to Bayes' theorem.