| Clinical trials are complex and usually involve multiple objectives such as controlling type I error rate, increasing power, protecting more patients from inferior treatments, etc. In literature, both response-adaptive randomization (RAR) procedures and sequential monitoring have been proposed to achieve these objectives to some degree. In this thesis, we propose to sequentially monitor response-adaptive randomized clinical trials using doubly-adaptive biased coin designs (DBCD) or urn models. We prove that the sequential test statistics of the new procedure converge to a Brownian motion in distribution under both the null and the alternative hypotheses. Further, we show that the sequential test statistics asymptotically satisfy the canonical joint distribution defined in Jennison and Turnbull (2000), Therefore, type I error and other objectives can be achieved theoretically by selecting appropriate boundaries. These results open a door to sequentially monitor response-adaptive randomized clinical trials in practice. The simulation studies show that the proposed procedure possesses the advantages of both techniques, in dealing with power, total sample size and total failure numbers, while keeps the type I error.;The second part of the thesis is to find the optimal allocation strategies for continuous response with multiple treatments under some optimization criteria. Here, we focus on exponential responses. For a multivariate test of homogeneity, we obtain the optimal allocation strategies to maximize power while (1) fixing sample size and (2) fixing expected total responses. Then the doubly adaptive biased coin design is used to implement the optimal allocation strategies. Simulation results show that the proposed procedures have advantages over complete randomization with respect to both inferential (power) and ethical standpoints on average. |
