Optimal Failure-Success Response-Adaptive Designs for Binary Responses
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Lanju Zhang Department of Biostatics, MedImmune Inc., Gaithersburg, Maryland Atanu Biswas Applied Statistics Unit, Indian Statistical Institute, Kolkata, India
Key Words Doubly adaptive biased coin design; Odds ratio; Optimal allocation; Urn design Correspondence Address Lanju Zhang, Department of Biostatics, MedImmune Inc., One MedImmune Way, Gaithersburg, MD 20878 (e-mail: [email protected], [email protected]).
Optimal FailureSuccess ResponseAdaptive Designs for Binary Responses
INTRODUCTION Response-adaptive randomization procedures can reduce the number of patients receiving inferior treatment by skewing the allocation probability to the better-performing treatment in the course of the trial with sequential arrival of patients. Since such clinical trials are intended to be unbalanced and skewed in favor of the better treatment, it is a fundamental problem to choose an appropriate allocation proportion. Obviously, the allocation proportion depends on the efficacy of the treatments, which most often is determined by the parameters of the concerned distributions of treatment responses. Although ethical concern requires an allocation proportion of more patients being allocated to the better-performing treatment, the power of the trial could be sacrificed by extreme imbalance and the correlation structure among patient responses induced by response-adaptive randomization. Therefore, there is a trade-off between the reduction in number of patients receiving inferior treatment and the preservation of power. A balance is needed in this context, which depends on an appropriate choice of allocation rules. A simple and important case of clinical trial outcomes is binary responses, designated by either success or failure. An allocation rule for binary responses can be the Neyman alloca-
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We generalize allocation rules of responseadaptive randomization designs for binary responses into three classes, covering many existing designs such as urn models and the optimal designs. The choice of the design parameters is discussed. The asymptotic variance of the allocation proportions of these designs is also derived. These designs are compared theoretically and numerically.
tion, which is defined in the section “FailureSuccess Designs From a General Formulation.” For Neyman allocation, more patients may be allocated to the inferior treatment, and consequently, the allocation will be unethical (1). The limiting proportion of allocations of popular urn models is another class of possibility. For some well-known urn designs, such as the randomized play-the-winner rule of Ref. 2 and the drop-the-loser rule of Ref. 3, the limiting allocation proportion is inversely proportional to the failure rate of the other treatment. Therefore, we will call this failure allocation design (FAD). However, Rosenberger et al. (4) propose the optimal allocation, which is proportional to the square root of the success rate of the treatments. Therefore, we will call this success allocation design (SAD). These two types of designs are discusse
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