Bayesian Sequential Randomization Designs for Phase III Clinical Trials

The use of Bayesian adaptive designs is becoming more popular due to its flexibility and efficiency. However, it is important to control the inflation of the type I error rate in the design. Several research have proposed methods to control the overall type I error rate in Bayesian adaptive design. In this dissertation, we proposed two Bayesian adaptive designs. One is a Bayesian sequential design using alpha spending functions to control the overall type I error for both continuous and binary outcomes (BSDASF and BSDASFB, respectively). The other is a Bayesian sequential design using adaptive randomization rates (BSDAR). We provided algorithms to calculate critical values, randomization rates, power and sample sizes for the proposed designs. Sensitivity analyses were also used to check the effects of different prior distributions and parameters on analysis results.;We compared the power and actual sample sizes of different alpha spending functions in the BSDASF and BSDASFB designs through simulations. We also compared the power of hypothesis tests using the proposed designs with that using the frequentist sequential designs under the same alpha spending function. Simulation studies showed that, at the same sample size, the testing power of the proposed design is greater than that of the corresponding frequentist sequential designs. For continuous or binary outcome, the proposed design has greater power than traditional Bayesian sequential design which sets equal critical values for all interim analyses. Further, we discussed the effects of adding stopping for futility rule in the proposed designs and proposed a new stopping for futility rule. We found that the proposed design with the new stopping for futility rule results in greater power of tests at given sample size and has the potential to stop early with a smaller actual sample size, compared with the same design but using traditional stopping for futility rule. In the BSDAR, the randomization rate for assigning patients can be changed to increase the overall power of tests at a given sample size. The simulation studies showed that, when total sample size is fixed, the BSDAR can further increase the power of tests compared with the BSDASF that uses equal randomization rates. We applied the proposed designs to real data sets and compare the results with that from traditional designs.