Brick tunnel randomization for unequal allocation to two or more treatment groups

Studies with unequal allocation to two or more treatment groups often require a large block size for permuted block allocation. This could present a problem in small studies, multi-center studies, or adaptive design dose-finding studies. In this paper, an allocation procedure, which generalizes the maximal procedure by Berger, Ivanova, and Knoll to the case of K≥2 treatment groups and any allocation ratio, is offered. Brick tunnel (BT) randomization requires the allocation path drawn in the k-dimensional space to stay close to the allocation ray that corresponds to the targeted allocation ratio. Specifically, it requires the allocation path to be confined to the set of the k-dimensional unitary cubes that are pierced by the allocation ray (the 'brick tunnel'). The important property of the BT randomization is that the transition probabilities at each node within the tunnel are defined in such a way that the unconditional allocation ratio is the same for every allocation step. This property is not necessarily met by other allocation procedures that implement unequal allocation.