Abstract
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. 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. 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. 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. 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. The numerical approach uses a sandwich-type searching algorithm, which immensely reduces the computational burden. We apply least-square fitting to find the α-spending function closest to the target. We discuss the application of our method to single-arm and double-arm cases with binary and normal endpoints, respectively, and provide a real trial example for each case.
Highlights
Along with the frequentist method, one of the popular paradigms in clinical trial designs is the Bayesian approach, where samples are treated as fixed and the parameter of interest is assigned a prior probability distribution to represent the uncertainty about its value; see, e.g., Berry (2006, 2011), Berger and Berry (1988), Efron (1986, 2005) and Yin (2012)
Based on the theoretical results, we propose a method to find the set of ck by connecting the Bayesian and the frequentist group sequential designs
In addition to the single-arm Bayesian sequential design, we study the properties of a double-arm Bayesian sequential design that uses the posterior probability at the interim analyses
Summary
Along with the frequentist method, one of the popular paradigms in clinical trial designs is the Bayesian approach, where samples are treated as fixed and the parameter of interest is assigned a prior probability distribution to represent the uncertainty about its value; see, e.g., Berry (2006, 2011), Berger and Berry (1988), Efron (1986, 2005) and Yin (2012). Inferences are made based on the posterior distribution of the parameter of interest, which can be updated as the trial accumulates more data. Along this direction, Thall and Simon (1994) proposed a Bayesian single-arm phase II clinical trial design that continually evaluates the posterior probability that the experimental drug is superior to the standard of care, where the response rate of the new treatment is compared with a fixed cutoff boundary at each interim analysis during the trial.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.