Optimal randomization and randomization test for multi-treatment clinical trials

Randomization plays an important role in both the design and analysis of clinical trials. First, the dissertation addresses one fundamental question in response-adaptive randomization: what allocation proportion we should target to achieve required power while resulting in fewer treatment failures. For comparing two treatments, such optimal allocations are well studied in the literature. However, generalization to multiple treatments is necessary in practice. We are interested in finding the optimal allocation proportion, which achieves a desired power of a multivariate test of homogeneity in binary response experiments while minimizing expected treatment failures at the same time. We propose such an optimal allocation for three treatments by giving an analytical solution for the optimization problem. Numerical studies show that a response-adaptive randomization procedure that targets the proposed optimal allocation is superior to complete randomization. In addition to this ethically attractive allocation, optimal allocations for minimizing costs of clinical trials and for more accurate confidence intervals are also discussed.;Next, the dissertation focuses on randomization methods for testing treatments effects in clinical trials. We discuss how to conduct randomization tests for a subset of treatments, especially a pair of treatments. To obtain valid randomization inferences, one should use a conditional reference set of permutations that allows randomization only of the units assigned to the pair of treatments. However, standard randomization procedure is not feasible due to overwhelming amounts of computation. We propose new randomization testing method by which true difference in the pair of treatments can be assessed without other treatments' interference. The proposed method is theoretically well-founded and is computational feasible. Some numerical studies are presented. We also discuss some future research topics and additional issues on randomization in clinical trials.