Restricted Randomization in Studies with Unequal Allocation

• Activity Number: 635
• Type: Topic Contributed
• Date/Time: Thursday, August 13, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Biopharmaceutical Section
• Author(s): Olga M. Kuznetsova*
• Companies: Merck
• Keywords: Brick Tunnel Randomization ; Unequal Allocation ; Large Block Size ; Allocation Ratio Preserving Randomization ; Restricted Randomization, ; Imbalance in Treatment Totals

Abstract

The allocation space of an unequal allocation permuted block randomization can be quite wide. The development of unequal allocation procedures with a narrower allocation space is complicated by the need to preserve the unconditional allocation ratio at every step (ARP property). When the allocation paths are depicted on the K-dimensional unitary grid, where allocation to the j-th treatment is represented by a step along the j-th axis, the ARP property can be expressed in terms of the center of the probability mass after i allocations. For an ARP procedure that randomizes subjects to K treatment groups in w1: . :wK ratio, w1+...+wK=1, the coordinates of the center of the mass are (w1*i, ., wK*i). In this presentation the momentum with respect to the center of the probability mass (expected distance) is used to compare ARP procedures in how closely they approximate the target allocation ratio. It is shown that the 2-arm Brick Tunnel Randomization (BTR) by Kuznetsova and Tymofyeyev (2011) has the smallest momentum of all ARP procedures with the same allocation ratio. The resident and transition probabilities for 3-arm BTR are analytically derived.