Characterizing permuted block randomization as a big stick procedure

There are numerous approaches to randomizing patients to treatment groups in clinical trials. The most popular is permuted block randomization, and a newer and better class, which is gaining in popularity, is the so-called class of MTI procedures, which use a big stick to force the allocation sequence back towards balance when it reaches the MTI (maximally tolerated imbalance). Three prominent members of this class are the aptly named big stick procedure, Chen's procedure, and the maximal procedure. As we shall establish in this article, blocked randomization, though not typically cast as an MTI procedure, does in fact use the big stick as well. We shall argue that its weaknesses, which are well known, arise precisely from its improper use, bordering on outright abuse, of this big stick. Just as rocket powered golf clubs add power to a golf swing, so too does the big stick used by blocked randomization hit with too much power. In addition, the big stick is invoked when it need not be, thereby resulting in the excessive prediction for which permuted blocks are legendary. We bridge the gap between the MTI procedures and block randomization by identifying a new randomization procedure intermediate between the two, namely based on an excessively powerful big stick, but one that is used only when needed. We shall then argue that the MTI procedures are all superior to this intermediate procedure by virtue of using a restrained big stick, and that this intermediate procedure is superior to block randomization by virtue of restraint in when the big stick is invoked. The transitivity property then completes our argument.