Journal
ANNALS OF STATISTICS
Volume 37, Issue 5A, Pages 2543-2560Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/08-AOS655
Keywords
Response-adaptive designs; biased coin design; clinical trial; urn model; doubly adaptive biased coin design; power
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Funding
- National Science Foundation (USA) [DMS-03-49048]
- National Natural Science Foundation of China [10771192, 10828102]
- U.S. National Science Foundation [DMS-06-04229]
- Changjiang Visiting Professorship at Northeast Normal University in China
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Response-adaptive randomization hits 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.
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