Brick Tunnel Randomization

Abstract

Brick tunnel randomization (BTR) introduced by Kuznetsova and Tymofyeyev is designed for unequal allocation studies with an inconvenient allocation ratio that leads to a large block size. In this case, permuted block randomization provides poor approximation to the targeted allocation ratio throughout the enrollment. BTR approximates the target allocation ratio well by requiring the allocation path to be confined to the set of k ‐dimensional unitary cubes that are pierced by the allocation ray (the “brick tunnel”). Importantly, BTR is an allocation ratio preserving (ARP) procedure: it preserves the unconditional allocation ratio at every allocation. The two‐ and three‐arm BTR are the ARP procedures with the tightest allocation space among all allocation procedures with the same allocation ratio. The two‐arm BTR has the lowest momentum of all two‐arm ARP procedures with the same allocation ratio. Resident and transition probabilities of two‐ and three‐arm BTR can be analytically derived; for more than three arms, they can be calculated using numerical methods.