Bayesian and other biased-coin designs for sequential clinical trials

A relationship is established between the Bayesian biased-coin design suggested by Ball et al. (1993) [F. G. Ball, A. F. M. Smith, I. Verdinelli: Biased coin designs with a Bayesian bias, J. Statist. Plann. Inference 34 (1993), 403–421] and the randomized optimum design suggested by Atkinson (1982) [A. C. Atkinson: The comparison of designs for sequential clinical trials with covariate information, (under revision)]. Properties of the Bayesian design are found by simulation.