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Keywords: Adaptive design; interim analysis; power; type I error
Once scientific questions have been determined, other design features of clinical trials, including increasing the power while controlling the type I error rate, planning interim analysis, and achieving treatment balance among subgroups, will be either required or preferred. We propose to sequentially monitor the covariate adaptive randomization (CAR) procedures with sample size re-estimation (SSR) to satisfy a variety of design objectives of clinical trials. However, each of the three adaptive designs (sequential monitoring, CAR, and SSR) poses a challenge to the control of the type I error rate. We investigated how to utilize the advantages of the three adaptive methods and control the type I error rate at the meantime. We proved that the asymptotic joint distribution of the sequential statistics follows the asymptotic canonical joint distribution defined in Jennison and Turnbull (2000). Additionally, numerical studies demonstrated that our methods could control the type I error rate, increase the power, and lead to much-improved treatment balance across subgroups.