Efron’s Biased Coin Design Revisited: Statistical Properties, Randomization-Based Inference and Sequential Monitoring

Efron’s [2] biased coin design is a restricted randomization procedure for clinical trials. This randomization design balances treatment assignments throughout the course of the trial and mitigates selection and accidental biases [9]. The biased coin design, BCD(p), for a parameter p ∈ [1/2, 1], q = 1 − p is defined as:

Pr(δj+1 = 1|Dj) =  p, if Dj < 0,1/2, if Dj = 0, j = 0, 1, 2, . . .