Bayesian Approaches for Monitoring Clinical Trials with an Application to Toxoplasmic Encephalitis Prophylaxis

Abstract

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 methodology 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).

Bayesian statistics in medicine: a 25 year review

“…A third Institute of Statisticians Conference on Applied Bayesian Statistics was held in 1992, with the proceedings running to three issues of The Statistician. Medical application included graphical elicitation of priors for clinical trials [115], monitoring of clinical trials [116], drug safety [117], case-control studies in cancer epidemiology [118], back-calculation of the numbers infected in the HIV epidemic [119], dosage regimens in population pharmaco-kinetics [120], analysis of binary cross-over data [121] and modelling heterogeneity in environmental epidemiology [122].…”

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“…Within the Bayesian framework, several authors (e.g. Carlin et al, 1993) have proposed using the partial likelihood to obtain a posterior distribution for the treatment effect. However, the Cox model does not allow fully hierarchical modeling of stratumspecific baseline hazards (with stratum-specific frailties) because the baseline hazard is implicit in the partial likelihood computation.…”

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