Efficient randomized-adaptive designs

Abstract

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.

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

References in corpus (3)

• Asymptotic Properties of Covariate-Adjusted Adaptive Designs
• Asymptotics in randomized urn models
• Asymptotic theorems of sequential estimation-adjusted urn models

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• Sequential monitoring of response-adaptive randomized clinical trials
• A New Family of Covariate-Adjusted Response Adaptive Designs and their Asymptotic Properties
• On the almost sure convergence of adaptive allocation procedures
• Multi-objective optimal designs in comparative clinical trials with covariates: The reinforced doubly adaptive biased coin design
• On the Theory of Covariate-Adaptive Designs
• Revisiting Optimal Allocations for Binary Responses: Insights from Considering Type-I Error Rate Control
• Efficient Covariate-Adaptive Randomization with Smallest Selection Bias in Clinical Trials