![]() Decisions at analysis points are usually based on the posterior distribution of the treatment effect. If one instead uses a strict Bayesian approach, which is currently more accepted in the design and analysis of exploratory trials, then type I errors could be ignored and the designs could instead focus on the posterior probabilities of treatment effects of clinically-relevant values.īackground: Bayesian adaptive methods are increasingly being used to design clinical trials and offer several advantages over traditional approaches. If the designs only allow for early stopping for futility then adjustments to the stopping boundaries are not needed to control type I error. To demonstrate control of type I error in Bayesian adaptive designs, adjustments to the stopping boundaries are usually required for designs that allow for early stopping for efficacy as the number of analyses increase. An increase in the number of interim analyses that allowed for either early stopping for efficacy or futility generally increased type I error and decreased power.Ĭurrently, regulators require demonstration of control of type I error for both frequentist and Bayesian adaptive designs, particularly for late-phase trials. An increase in the number of interim analyses that only allowed early stopping for futility decreased the type I error, but also decreased power. Incorporation of early stopping for efficacy also increased the power in some instances. In both case studies we demonstrated that the type I error was inflated in the Bayesian adaptive designs through incorporation of interim analyses that allowed early stopping for efficacy and without adjustments to account for multiplicity. We propose several approaches to control type I error, and also alternative methods for decision-making in Bayesian clinical trials. ![]() With two case studies we illustrate the effect of including interim analyses on type I/II error rates in Bayesian clinical trials where no adjustments for multiplicities are made. We discuss the arguments for and against adjusting for multiplicities in Bayesian trials with interim analyses. However, there is some confusion as to whether control of type I error is required for Bayesian designs as this is a frequentist concept. We discuss the application of our method to single-arm and doublearm cases with binary and normal endpoints, respectively, and provide a real trial example for each case.īayesian adaptive methods are increasingly being used to design clinical trials and offer several advantages over traditional approaches. We apply least-square fitting to find the α-spending function closest to the target. The numerical approach uses a sandwich-type searching algorithm, which immensely reduces the computational burden. The theoretical approach is based on the asymptotic properties of the posterior probability, which establishes a connection between the Bayesian trial design and the frequentist group sequential method. We present both theoretical and numerical methods for finding the optimal posterior probability boundaries with α-spending functions that mimic those of the frequentist group sequential designs. To effectively maintain the overall type I error rate, we propose solutions to the problem of multiplicity for Bayesian sequential designs and, in particular, the determination of the cutoff boundaries for the posterior probabilities. If the posterior probability is computed and assessed in a sequential manner, the design may involve the problem of multiplicity, which, however, is often a neglected aspect in Bayesian trial designs. Bayesian approaches to phase II clinical trial designs are usually based on the posterior distribution of the parameter of interest and calibration of certain threshold for decision making.
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