Abstract
SUMMARY Biased coin designs are used in clinical trials as a means of achieving approximate balance within a randomized design. In this paper, detailed results are obtained for a class of biased coin designs from the point of view of the degree of balance achieved, selection bias, accidental bias and inference following the randomized trial. These results are developed in detail for the simple situation with two treatments and no prognostic factors. They are then extended to cover (i) more than two treatments with no prognostic factors, (ii) two treatments with prognostic factors.
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