A dynamic block-randomization algorithm for group-randomized clinical trials when the composition of blocking factors is not known in advance

We present an algorithm for randomizing units in blocks for controlled trials when the composition of blocking factors is not known in advance. For example, suppose the desired goal of an intervention study is to randomize units to one of two interventions while blocking on a dichotomous factor (e.g., gender), but the total number of units, and therefore number or composition, of males and females among those units assembled for randomization cannot be determined in advance. This situation arises in randomized trials when subjects are scheduled to be randomized as a group, but not all of the subjects show up for the visit. Since investigators do not know which of the scheduled subjects will or will not show up, a dynamic randomization scheme is required to accommodate the unknown composition of the blocking factor once a group of subjects (units) is assembled for randomization. These settings are further complicated when there is more than one blocking factor. In this paper, we present an algorithm that ensures the integrity of the randomization process in these settings.