Generalization of Wei's urn design to unequal allocations in sequential clinical trials

Wei's urn design was proposed in 1987 for subject randomization in trials comparing m ≥ 2 treatments with equal allocation. In this manuscript, two modified versions of Wei's urn design are presented to accommodate unequal allocations. First one uses a provisional allocation of r12:r22 to achieve the target allocationr1:r2, and the second one uses equal allocation for r1 + r2 arms to achieve an unequal allocationr1:r2 based on the concept Kaiser presented in his recent paper. The properties of these two designs are evaluated based on treatment imbalance and allocation predictability under different sample sizes and unequal allocation ratios. Simulations are performed to compare the two designs to other designs used for unequal allocations, include the complete randomization, permuted block randomization, block urn design, maximal procedure, and the mass weighted urn design.