The Covariate-Adaptive Biased Coin Design for balancing clinical trials in the presence of prognostic factors

The present paper deals with sequential designs intended to balance the allocations of two competing treatments in the presence of prognostic factors. After giving a theoretical framework on the optimality of balanced designs that can arise when covariates are taken into account, we propose a new family of covariate-adaptive randomized designs that represents higher order approximation to balance treatments, both globally and also across covariates. We derive the theoretical properties of the suggested designs in terms of loss of precision and predictability. The performance of this proposal is illustrated through a simulation study and compared with those of other procedures suggested in the literature.