Response adaptive designs with a variance-penalized criterion

We consider a response adaptive design of clinical trials with a variance-penalized criterion. It is shown that this criterion evaluates the performance of a response adaptive design based on both the number of patients assigned to the better treatment and the power of the statistical test. A new proportion of treatment allocation is proposed and the doubly biased coin procedure is used to target the proposed proportion. Under reasonable assumptions, the proposed design is demonstrated to generate an asymptotic variance of allocation proportions, which is smaller than that of the drop-the-loser design. Simulation comparisons of the proposed design with some existing designs are presented.