Nonparametric Bayesian Group Sequential Design
The customary objective of a group sequential design is the comparison of several treatments or populations. The evolutionary nature of such trials encourages the use of the Bayesian paradigm in the design, monitoring and analysis of these trials. Here we focus on the design issue for the case of continuous, possibly multivariate response at each trial. Our approach is descriptive. Given a model specification, a design is characterized by a number of interim evaluations, the group size for each interim look, and a set of stopping criteria which determine our decision at a given look. By simulating replications of the design we can summarize design performance in terms of when the trial was stopped and reason for stopping. Such simulation and evaluation requires a fully Bayesian model specification for each treatment. We take a nonparametric perspective for the likelihood specification by assuming that the data is drawn from a distribution which arises through Dirichlet process mixing. However, we distinguish a sampling or “what if” prior, reflecting illustrative differences between populations, from a fitting or skeptical prior assuming no differences. By drawing trials under the sampling model, while fitting the model under the fitting prior, Bayesian learning moves us from prior indifference to detection of differences. We illustrate with two examples, one having univariate response, the other bivariate response.
KeywordsGibbs Sampler Patient Response Under Sampling Dirichlet Process Sampling Prior
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- Carlin, B. P., Kadane, J. B., and Gelfand, A. E. (1998), “Approaches for Optimal Sequential Decision Analysis in Clinical Trials”, Biometrics (to appear). Google Scholar
- Escobar, M. D. and West, M. (1992), “Computing Bayesian Nonparametric Hierarchical Models”, Technical report, ISDS, Duke University.Google Scholar
- Gelfand, A. E. and Vlachos, P. K. (1995), “Bayesian Clinical Trial Design for Multivariate Categorical Response Models”, Technical Report 9501, Department of Statistics, The University of Connecticut.Google Scholar
- Kadane, J. B. and Vlachos, P. K. (1998), “Hybrid Methods for Calculating Optimal Sequential Strategies: Data Monitoring for a Clinical Trial”, Technical report, Carnegie Mellon University.Google Scholar
- Lewis, R. J. and Berry, D. A. (1994), “Group Sequential Clinical Trials: A Classical Evaluation of Bayesian Decision-Theoretic Design”, Journal of the American Statistical Association. Google Scholar
- Spiegelhalter, D. J. and Freedman, L. S. (1988), “Bayesian Approaches to Clinical Trials (with discussion)”, in Bayesian Statistics 3 (eds: Bernardo, J.M., Berger, J.O., DeGroot, M., and Smith, A.F.M.), Oxford University Press, 453–477.Google Scholar
- Vlachos, P. K. and Gelfand, A. E. (1996), “Bayesian Decision Theoretic Design for Group Sequential Medical Trials Having Multivariate Patient Response”, Technical Report 96–03, Department of Statistics, The University of Connecticut.Google Scholar