Bayesian interpretation of trials: the example of intrapartum electronic fetal heart rate monitoring

Bayes’ theorem tells us how to update our knowledge about the chance of an event, in the light of new evidence. Doctors use it when deciding whether a patient has a disease, given a particular test result. The formula is: prior odds of the disease times the likelihood ratio of the test result equals posterior odds. Whether or not we understand the mathematical details, we cannot avoid the main idea that the implication of a test varies with the prior risk. For example, an abnormal fetal umbilical artery Doppler waveform is much more likely to indicate a problem if the woman is hypertensive or bleeding, than if the test is done to screen a healthy pregnancy. Similarly, a two millimetre fetal nuchal pad measurement at 12 weeks of gestation for a 40 year old woman indicates a 1 in 160 risk of Down’s syndrome, but the same test result on a 20 year old indicates only a 1 in 1900 risk. Similar methods of thinking can be used to interpret randomised controlled trials’. Often we already have some expectation that a new treatment will be beneficial, either from previous trials, observational studies or our understanding of the underlying biology. We may not be certain, but neither are we completely ignorant. A researcher who adopts a Bayesian perspective assesses these prior beliefs and uses the trial data to modify them. The consequences are important. Since peoples’ prior beliefs may differ, their final beliefs at the end of the trial may also differ. This makes some people uncomfortable, and means that Bayesians need to take as much care justifying their prior beliefs as they do over other aspects of trial design. Another consequence of Bayesian analysis is that there is no longer any ovemding statistical reason to conceal interim trial results from participants or to limit the number of interim analyses. People with different prior beliefs, and different minimal worthwhile effect sizes, (see ‘delta’ below) will decide to stop at different points. This means that Bayesians differ over whether they reveal interim results. Purists insist that all results should be completely open on ethical grounds, arguing that it is wrong to permit some clinicians to go on randomising when, if they knew the interim results, they would no longer be uncertain. More pragmatic Bayesians sometimes conceal results for fear that clinicians will over-interpret them and lower recruitment. All Bayesians need to collect evidence in reliable ways, usually by using secure methods of randomisation, and avoiding selective publication of positive results.