Graphical Elicitation of a Prior Distribution for a Clinical Trial

Bayesian methods are potentially useful for the design, monitoring and analysis of clinical trials. These methods, however, require that prior information be quantified and that the methods be robust. This paper describes a method to help quantify beliefs in the form of a prior distribution about regression coefficients in a proportional hazards regression model. The method uses dynamic graphical displays of probability distributions that can be freehand adjusted. The method was developed for, and is applied to, a randomized trial comparing prophylaxes for toxoplasmosis in a population of HIV-positive individuals. Prior distributions from five AIDS experts are elicited. The experts represent a community of consumers of the results of the trial and these prior distributions can be used to try to make the monitoring and analysis of the trial robust. Bayesian approaches to clinical trials, as discussed for example by Spiegelhalter and Freedman (1988) and Freedman and Spiegelhalter (1992), require the specification of a prior distribution. In this paper, an AIDS clinical trial comparing potential prophylaxes for toxoplasmosis is used as a context to develop and implement methodology to aid in the elicitation of prior distributions. Following Kadane (1986), we require that a range of priors be identified that are representative of 'the community'. These will then be used to try to make monitoring and analysis robust. This paper focuses on the elicitation part of such an approach, and we report on the prior distributions of five individuals. Bayesian analysis and monitoring of the trial is reported in Carlin et al. (1993). First, we provide a description of the toxoplasmosis prophylaxis trial and then describe the elicitation method based on graphical input and feedback. We then summarize what we learned from eliciting the prior distributions, the results of the trial, and some of the problems in implementing a Bayesian approach.