Bayesian approaches for monitoring clinical trials with an application to toxoplasmic encephalitis prophylaxis

Bayesian methods have been a subject of increasing interest among researchers engaged in the interim monitoring and final analysis of clinical trials data. In particular, Chaloner et al. (1992) have shown how prior distributions may be elicited relatively easily from a panel of experts using computer-assisted interactive graphical methods. Significant stumbling blocks remain, however, to routine implementation of Bayesian methods by practitioners. For example, heavy computational burdens have historically precluded real-time evaluation of stopping rules. In addition, the resulting statistics may not be amenable to simple monitoring displays, since the resulting posterior distributions for important model parameters need not be symmetric, unimodal or based on a low-dimensional sufficient statistic. In this paper we investigate these computational issues by comparing the posterior distributions of model parameters obtained assuming approximate posterior normality with more precise results obtained via numerical integration. We also investigate the impact of approximations on the performance of Bayesian stopping rules. Where the normal approximation is inappropriate, the Bayesian methodology still allows for inference and simple monitoring displays based on posterior probabilities. We illustrate the methodol- ogy with a numerical example featuring prior distributions elicited from five AIDS experts and data from a recently completed toxoplasmic encephalitis prophylaxis trial (Jacobson et al., 1992).