The Annals of Statistics

Efficient randomized-adaptive designs

Feifang Hu, Li-Xin Zhang, and Xuming He

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Response-adaptive randomization has recently attracted a lot of attention in the literature. In this paper, we propose a new and simple family of response-adaptive randomization procedures that attain the Cramer–Rao lower bounds on the allocation variances for any allocation proportions, including optimal allocation proportions. The allocation probability functions of proposed procedures are discontinuous. The existing large sample theory for adaptive designs relies on Taylor expansions of the allocation probability functions, which do not apply to nondifferentiable cases. In the present paper, we study stopping times of stochastic processes to establish the asymptotic efficiency results. Furthermore, we demonstrate our proposal through examples, simulations and a discussion on the relationship with earlier works, including Efron’s biased coin design.

Article information

Ann. Statist., Volume 37, Number 5A (2009), 2543-2560.

First available in Project Euclid: 15 July 2009

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Zentralblatt MATH identifier

Primary: 60F15: Strong theorems 62G10: Hypothesis testing
Secondary: 60F05: Central limit and other weak theorems 60F10: Large deviations

Response-adaptive designs biased coin design clinical trial urn model doubly adaptive biased coin design power


Hu, Feifang; Zhang, Li-Xin; He, Xuming. Efficient randomized-adaptive designs. Ann. Statist. 37 (2009), no. 5A, 2543--2560. doi:10.1214/08-AOS655.

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