Bayesian treatment comparison using parametric mixture priors computed from elicited histograms
A pervasive problem in randomized clinical trials in children or rare diseases is that the sample size often is too small to obtain a confirmatory conclusion using conventional statistical methods. We propose a Bayesian methodology for constructing a parametric prior on two treatment effect parameters, based on information elicited from expert physicians. The motivating application is a 70-patient randomized trial to compare two treatments for idiopathic nephrotic syndrome in children. Before the trial, 17 experts provided their opinions about the treatment effect for each arm constructing manually histograms using the “bins-and-chips” graphical method. For each physician and treatment, a marginal prior, characterized by location and precision, was fit to each elicited histogram. Bivariate expert-specific priors were constructed using two correlated latent expert effects, using either of two proposed methods.
An overall prior was constructed as a mixture of the individual physicians’ priors, with three possible weighting schemes. A framework was provided for performing a sensitivity analysis of posterior inferences to prior bias and precision. A simulation study evaluating several versions of the methodology for binary outcomes was presented. The methodology provides a practical way to incorporate expert opinion, with the prior-to-posterior sensitivity analysis allowing non-statisticians to draw their own conclusions in an informed way.