Title: Bayesian Adaptive Methods for Clinical Trials Instructor: Brad Carlin, University of Minnesota Overview: Thanks in large part to the rapid development of Markov chain Monte Carlo (MCMC) methods and software for their implementation, Bayesian methods have become ubiquitous in modern biostatistical analysis. In submissions to regulatory agencies where data on new drugs or medical devices are often scanty but researchers have access to large historical databases, Bayesian methods have emerged as particularly helpful in combining the disparate sources of information while maintaining traditional frequentist protections regarding Type I error and power. Biostatisticians in earlier phases (especially Phase I oncology trials) have long appreciated Bayes' ability to get good answers quickly. Finally, an increasing desire for adaptability in clinical trials (to react to trial knowledge as it accumulates) has also led to heightened interest in Bayesian methods. This lecture series introduces Bayesian methods, computing, and software, and then goes on to elucidate their use in Phase I and II clinical trials. We include desc-riptions of how the methods can be implemented in WinBUGS, R, and BRugs, a version of the BUGS package callable from within R. Lecture 1: Introduction to Hierarchical Bayes Methods and Computing Bayesian inference: point and interval estimation, model choice Bayesian computing: MCMC methods; Gibbs sampler; Metropolis-Hastings algorithm Hierarchical modeling and metaanalysis Principles of Bayesian clinical trial design: predictive probability, indifference zone, Bayesian and frequentist operating characteristics (power, Type I error) Lecture 2: Bayesian design and analysis for Phase I studies Rule-based designs for determining the MTD (e.g., 3+3) Model-based designs for determining the MTD (CRM, EWOC, TITE monitoring, toxicity intervals) Dose ranging and optimal biologic dosing Efficacy and toxicity Examples and software Lecture 3: Bayesian design and analysis for Phase II studies Standard designs: Phase IIA (single-arm) vs. Phase IIB (multi-arm) Predictive probability-based methods Sequential stopping: for futility, efficacy Multi-arm designs with adaptive randomization Adaptive confirmatory trials: adaptive sample size, futility analysis, arm dropping Bayesian hierarchical methods in safety studies Adaptive incorporation of historical data Summary and Floor Discussion