A theoretical analysis of the power of biased coin designs

Outlining some recently obtained results of Hu and Rosenberger [2003. Optimality, variability, power: evaluating response-adaptive randomization procedures for treatment comparisons. J. Amer. Statist. Assoc. 98, 671–678] and Chen [2006. The power of Efron's biased coin design. J. Statist. Plann. Inference 136, 1824–1835] on the relationship between sequential randomized designs and the power of the usual statistical procedures for testing the equivalence of two competing treatments, the aim of this paper is to provide theoretical proofs of the numerical results of Chen [2006. The power of Efron's biased coin design. J. Statist. Plann. Inference 136, 1824–1835]. Furthermore, we prove that the Adjustable Biased Coin Design [Baldi Antognini A., Giovagnoli, A., 2004. A new “biased coin design” for the sequential allocation of two treatments. J. Roy. Statist. Soc. Ser. C 53, 651–664] is uniformly more powerful than the other “coin” designs proposed in the literature for any sample size.