'Optimal' Randomized Designs for Sequential Experiments with Two Treatments

This paper starts with a discussion of the ``optimality'' of sequential randomized designs for comparing two treatments and introduces the concept\ of ``desirable'' proportion of allocations to one of the treatments. The problem is finding a randomized design which converges to the desirable one almost certainly and also forces the procedure towards the desirable proportion even for small samples. When balance is optimal we show that Efron's Biased Coin Design (1971) and the class of Wei's designs (1978) are asymptotically desirable and propose extensions of the above mentioned algorithms that converge almost surely to any desired proportion, when the value is known. The Adjustable Biased Coin Design of Baldi Antognini and Giovagnoli (2003) also converges to balance and the convergence is faster than the other procedures.