Some Optimal Adaptive Designs in Clinical Trials

We consider the clinical trials scenario where patients enter the trial sequentially, and the experimenter has to adaptively select the better of the two competing treatments for future applications. This is particularly important since the subjects are human patients. In this article, based on the statistical validity, we discuss several optimal allocation rules in the clinical trial, which depend on unknown parameters. Then, the corresponding adaptive design is proposed, and, some asymptotic properties are obtained. With these asymptotic results, we show that the adaptive designs in this article lead to the asymptotically optimal allocations.