Efficient randomized-adaptive designs

Details Efficient randomized-adaptive designs Efficient randomized-adaptive designs

2009-08-24

arxiv.org/abs/0908.3435v1

Annals of Statistics 2009, Vol. 37, No. 5A, 2543-2560

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/08-AOS655 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/08-AOS655

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.

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