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May 2015 On the almost sure convergence of adaptive allocation procedures
Alessandro Baldi Antognini, Maroussa Zagoraiou
Bernoulli 21(2): 881-908 (May 2015). DOI: 10.3150/13-BEJ591

Abstract

In this paper, we provide some general convergence results for adaptive designs for treatment comparison, both in the absence and presence of covariates. In particular, we demonstrate the almost sure convergence of the treatment allocation proportion for a vast class of adaptive procedures, also including designs that have not been formally investigated but mainly explored through simulations, such as Atkinson’s optimum biased coin design, Pocock and Simon’s minimization method and some of its generalizations. Even if the large majority of the proposals in the literature rely on continuous allocation rules, our results allow to prove via a unique mathematical framework the convergence of adaptive allocation methods based on both continuous and discontinuous randomization functions. Although several examples of earlier works are included in order to enhance the applicability, our approach provides substantial insight for future suggestions, especially in the absence of a prefixed target and for designs characterized by sequences of allocation rules.

Citation

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Alessandro Baldi Antognini. Maroussa Zagoraiou. "On the almost sure convergence of adaptive allocation procedures." Bernoulli 21 (2) 881 - 908, May 2015. https://doi.org/10.3150/13-BEJ591

Information

Published: May 2015
First available in Project Euclid: 21 April 2015

zbMATH: 1320.62189
MathSciNet: MR3338650
Digital Object Identifier: 10.3150/13-BEJ591

Rights: Copyright © 2015 Bernoulli Society for Mathematical Statistics and Probability

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Vol.21 • No. 2 • May 2015
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