Wide brick tunnel randomization - an unequal allocation procedure that limits the imbalance in treatment totals.

In open-label studies, partial predictability of permuted block randomization provides potential for selection bias. To lessen the selection bias in two-arm studies with equal allocation, a number of allocation procedures that limit the imbalance in treatment totals at a pre-specified level but do not require the exact balance at the ends of the blocks were developed. In studies with unequal allocation, however, the task of designing a randomization procedure that sets a pre-specified limit on imbalance in group totals is not resolved. Existing allocation procedures either do not preserve the allocation ratio at every allocation or do not include all allocation sequences that comply with the pre-specified imbalance threshold. Kuznetsova and Tymofyeyev described the brick tunnel randomization for studies with unequal allocation that preserves the allocation ratio at every step and, in the two-arm case, includes all sequences that satisfy the smallest possible imbalance threshold. This article introduces wide brick tunnel randomization for studies with unequal allocation that allows all allocation sequences with imbalance not exceeding any pre-specified threshold while preserving the allocation ratio at every step. In open-label studies, allowing a larger imbalance in treatment totals lowers selection bias because of the predictability of treatment assignments. The applications of the technique in two-arm and multi-arm open-label studies with unequal allocation are described.