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Generalized Efron's biased coin design and its theoretical properties

Part of: Limit theorems Applications

Published online by Cambridge University Press:  21 June 2016

Yanqing Hu
Yanqing Hu*
Affiliation:
West Virginia University
*
* Postal address: Department of Statistics, West Virginia University, PO Box 6330, Morgantown, WV 26506, USA. Email address: [email protected]
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Abstract

In clinical trials with two treatment arms, Efron's biased coin design, Efron (1971), sequentially assigns a patient to the underrepresented arm with probability p > ½. Under this design the proportion of patients in any arm converges to ½, and the convergence rate is n-1, as opposed to n-½ under some other popular designs. The generalization of Efron's design to K ≥ 2 arms and an unequal target allocation ratio (q1, . . ., qK) can be found in some papers, most of which determine the allocation probabilities ps in a heuristic way. Nonetheless, it has been noted that by using inappropriate ps, the proportion of patients in the K arms never converges to the target ratio. We develop a general theory to answer the question of what allocation probabilities ensure that the realized proportions under a generalized design still converge to the target ratio (q1, . . ., qK) with rate n-1.

Keywords

More than two treatmentsunequal allocationdrift conditionsMarkov chain

MSC classification

Primary: 60F99: None of the above, but in this section
Secondary: 62P10: Applications to biology and medical sciences
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 2 , June 2016 , pp. 327 - 340
Copyright
Copyright © Applied Probability Trust 2016 

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