Statistics and Its Interface

Volume 1 (2008)

Number 1

Optimal biased coins for two-arm clinical trials

Pages: 125 – 135



Thomas Gwise (E.)

Feifang Hu (Department of Statistics, University of Virginia, Charlottesville, Va., U.S.A.)

Jianhua Hu (Anderson Cancer Center, U.S.A.)


Atkinson (1982) introduced $D$-optimal and $D_A$-optimal biased coin designs to achieve balanced allocation. In this paper, we relax the restrictive assumptions on Atkinson’s design so that it can be applied to more realistic situations of heteroscedastic data for two-arm clinic trials. A new class of adaptive biased coin designs is obtained. Further, we derive the asymptotic properties of the proposed allocation procedures, and show that the allocation targets maximizing power via a direct connection to Neyman’s allocation scheme. Simulation studies illustrate that the theoretical results are valid and that the proposed design has testing power that is superior to that of the completely randomized allocation scheme.


adaptive design, $D$-optimal biased coin, $D_A$-optimal biased coin, response adaptive design, continuous responses, binary responses

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