Concealing Block Sizes Is Not Sufficient.

Abstract

Editor: Kim and Shin1) correctly noted that blocked randomization has a disadvantage that the executer can predict next assignment and this is clearly incompatible with allocation concealment. So we can agree that permuted blocks with a fixed block size should never be used in randomized trials.2) But what is solution to this problem? Kim and Shin1) indicated that To solve this problem, allocator must hide block size form executer and use randomly mixed block This would be an ideal solution if our only objective were to minimize deterministic allocations. But some allocations are predictable even while not being entirely deterministic. For example, if block size is four, and identity of first treatment allocated is known, then second allocation is not deterministic, but it is still predictable, since it is twice as likely to be treatment that was not allocated first. These predictable allocations allow investigators betting odds, so even these must be minimized. The reality is that even with unusual, varied, and concealed block sizes, there will still be some deterministic allocations, and an abundance of predictable allocations. For example, suppose it is known that block sizes in a given unmasked trial are varied, two and four, and suppose that at a certain point in trial there are two more patients allocated to control group than to active group. Then it can be deduced that current block size is four, since a block of size two will never allow imbalance to exceed one. We also know that we are halfway through a CCAA block, so next two allocations must be to active group. But bigger issue is, as noted, large number of predictable allocations. Any randomization procedure that is restricted so as to force equal numbers allocated to each treatment group will be vulnerable to convergent strategy of guessing (without certainty) that next treatment to be allocated will be one so far less well represented. This is not particular to permuted blocks with either fixed or varied block sizes. However, varying block sizes will be more susceptible since there are smaller blocks (on average) than there would be with a fixed block size of largest size used. Hence, convergent strategy will be more effective with varied block sizes than it will be with fixed block sizes. Table 5.4 of Berger3) illustrates that fixed block sizes are better than varied block sizes when investigators use convergent strategy. But of course, as noted, permuted blocks with fixed block sizes should never be used.2) Clearly, then, neither should permuted blocks with varied block sizes.4) Fortunately, there is a better way to randomize. Specifically, maximal procedure5) has been amply demonstrated to be uniformly better than permuted blocks procedure for ensuring allocation concealment and controlling selection bias. It too is vulnerable to convergent strategy, but not nearly as much as permuted blocks procedure is, with either fixed or varied blocks, as quantified in Table 5.4 of Berger.3) Therefore, it is maximal procedure, and not varied or unusual or concealed block sizes, which is solution to problem of prediction.