ABSTRACT
Improper randomization, most notably permuted block randomization with its excessive set of restrictions, is known to compromise allocation concealment, thereby opening the door to a form of selection bias that can completely invalidate the trial. A great deal of recent work has focused on the so-called MTI (maximally tolerated imbalance) randomization procedures (including the big stick, Chen, maximal, and block urn procedures), as these are less restrictive and therefore correspondingly more resistant to selection bias, compared to permuted block randomization. Some researchers have argued that we need to go even further, since only unrestricted randomization can completely eliminate the type of selection bias we consider. Indeed, some authors point to the few trials that have used unrestricted randomization and lament the fact that more do not follow suit. While the goal of eliminating selection bias is certainly laudable, the advice is misguided, since unrestricted randomization never has been, and never will be, used in an actual trial, and this is how it has to be, for pragmatic reasons that we shall discuss. What is actually used, when unrestricted randomization is claimed, is a variation on this theme that cannot be identified, and therefore its properties remain unknown. We will clarify this seemingly bizarre claim by appealing to a new concept, namely, projections of one space of randomization sequences into another. We will conclude by noting that one interpretation, possibly the most reasonable one, of what is meant when unrestricted randomization is claimed is the maximal procedure. This finding strengthens the already compelling case for using the maximal procedure in Phase III randomized clinical trials.
