Reporting Bayesian analyses of clinical trials

Many clinicians wrongly interpret p-values as probabilities that treatment has an adverse effect and confidence intervals as probability intervals. Such inferences can be validly drawn from Bayesian analyses of trial results. These analyses use the data to update the prior (or pre-trial) beliefs to give posterior (or post-trial) beliefs about the magnitude of a treatment effect. However, for these methods to gain acceptance in the medical literature, understanding between statisticians and clinicians of the issues involved in choosing appropriate prior distributions for trial reporting needs to be reached. I focus on two types of prior that deserve consideration. The first is the non-informative prior giving standardized likelihood distributions as post-trial probability distributions. Their use is unlikely to be controversial among statisticians whilst being intuitively appealing to clinicians. The second type of prior has a spike of probability mass at the point of no treatment effect. Varying the magnitude of the spike illustrates the sensitivity of the conclusions drawn to the degree of prior scepticism in a treatment effect. With both, graphical displays provide clinical readers with the opportunity to explore the results more fully. An example of how a clinical trial might be reported in the medical literature using these methods is given.