## The Annals of Statistics

### Asymptotic properties of doubly adaptive biased coin designs for multitreatment clinical trials

#### Abstract

A general doubly adaptive biased coin design is proposed for the allocation of subjects to K treatments in a clinical trial. This design follows the same spirit as Efron's biased coin design and applies to the cases where the desired allocation proportions are unknown, but estimated sequentially. Strong consistency, a law of the iterated logarithm and asymptotic normality of this design are obtained under some widely satisfied conditions. For two treatments, a new family of designs is proposed and shown to be less variable than both the randomized play-the-winner rule and the adaptive randomized design. Also the proposed design tends toward a randomization scheme (with a fixed target proportion) as the size of the experiment increases.

#### Article information

Source
Ann. Statist., Volume 32, Number 1 (2004), 268-301.

Dates
First available in Project Euclid: 12 March 2004

Permanent link to this document
https://projecteuclid.org/euclid.aos/1079120137

Digital Object Identifier
doi:10.1214/aos/1079120137

Mathematical Reviews number (MathSciNet)
MR2051008

Zentralblatt MATH identifier
1105.62381

Subjects
Primary: 60F15: Strong theorems 62G10: Hypothesis testing

#### Citation

Hu, Feifang; Zhang, Li-Xin. Asymptotic properties of doubly adaptive biased coin designs for multitreatment clinical trials. Ann. Statist. 32 (2004), no. 1, 268--301. doi:10.1214/aos/1079120137. https://projecteuclid.org/euclid.aos/1079120137

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