Replacing permuted block design with big stick design in stratified randomization

The PBD (Permuted Block Design) is the most widely used randomization method in clinical trials due to its comparatively simplicity. However, greater selection bias may appear, especially in open-labeled trials, because the PBD requires absolute balance at the end of each block . The BSD(Big Stick Design) method is one of the MTI(Maximum Tolerated Imbalance) procedures, which can make the allocation process more unpredictable while maintaining the advantages the PBD. So it is theoretically superior to the PBD method. However, some practical problems in stratified randomization hinder the application of the BSD method: such as the risk of serious imbalance for entire trials with the increasing of strata, the uncertainty of the reproducibility of randomization schedule, and the danger of greater selection bias in extreme cases. We propose solutions to the above three implementation problems, and explores the feasibility and effects of the solutions through simulations.