Higher order response-adaptive urn designs for clinical trials with highly successful treatments

We consider a problem of reducing the expected number of treatment failures in trials where the probability of response to treatment is close to 1 and treatments are compared on the basis of the log-odds ratio. We propose a new class of urn designs for randomization of patients in a clinical trial. The new urn designs target a number of allocation proportions including the allocation proportion that yields the same power as equal allocation but significantly less expected treatment failures. The new design is compared with the doubly adaptive biased coin design, the efficient randomized adaptive design and with equal allocation. The properties of the new class of designs are studied by embedding them in a family of continuous time stochastic processes.