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  • Book
    Olivia Yueh-Wen Liao.
    When developing new drugs, Phase I and II trials are commonly conducted to determine the dose of the new treatment in preparation for the subsequent confirmatory Phase III trial. However, because these early-phase trials usually do not have large enough sample sizes to decide which dosage level or treatment regimen is the best, several of them may arise as candidates for the confirmatory Phase III trial. Conventional fixed sample size designs that carry out all the treatment arms of interest are obviously expensive. Therefore, the pharmaceutical industry is increasingly interested in adaptive designs that can use information acquired during the course of the trial to update certain of the design features. In this thesis we explore several existing designs and discuss their pros and cons. We then propose one that shares the flexibility of Bayesian adaptive designs, while still being able to maintain the frequentist type I error probability. We develop an asymptotic theory for efficient outcome-adaptive randomization schemes and optimal stopping rules. Our approach consists of developing asymptotic lower bounds for the expected sample sizes from the treatment arms and the control arm, and using generalized sequential likelihood ratio procedures to achieve these bounds. These allow us to allocate patients and study resources efficiently by using outcome-adaptive randomization schemes, or by arm suspension/selection if fixed randomization is used. We also derive an adaptive test with a p-value that can be evaluated by Monte Carlo simulation based on an ordering scheme of the sample space. We then show that the approach can also be applied to the closely related problem of multi-stage testing of multiple hypotheses.