Practical Reporting of Bayesian Analyses of Clinical Trials

Abstract

Agreement on appropriate ways of presenting Bayesian analyses of clinical trials is essential if these methods are to obtain more widespread use and not fall into disrepute. Using an example based upon a trial currently in progress, two aspects of reporting are proposed. Using noninformative priors gives standardized likelihoods from which point and interval estimates, and probabilities associated with adverse effects, can be obtained with numerically similar values to classical estimates, confidence intervals, and p-values. Standardized likelihoods are therefore a useful means of introducing Bayesian analyses into trial reports and emphasizing the change in interpretation to quantifying beliefs. The second important use of Bayesian analyses is to illustrate strength of evidence coming from a trial by showing the sensitivity of the conclusions drawn to choice of prior distribution made. This can be achieved by employing other well–defined priors, notably that based on previous trial results and that reflecting investigators' opinions. However, this may not be sufficient to convince clinicians in general of an effect and so produce a real change in clinical practice. A method which relates the strength of evidence for a beneficial effect to the degree of prior scepticism in no effect is therefore proposed to address this.