Matched randomization in RCTs where subjects trickle in one at a time or in small batches
*Robert Alan Greevy, Vanderbilt University 

Keywords: restricted randomization, nonbipartite matching, Mahalanobis distance, randomized controlled trials

Pure randomization continues to be widely used in randomized controlled trials where subjects trickle in one at a time or in small batches. Moreover, when restricted randomization is used, a block randomization or a stratified design that conditions the randomization on only one or two covariates is most often applied. These designs balance on only a couple of the important covariates resulting in designs that are less efficient on average and have non-trivial probabilities of creating an imbalance on an important covariate. Biased coin designs, such as that proposed in Pocock and Simon’s 1975 Biometrics paper, have the benefit of conditioning the randomization on many covariates while still working to balance the number of subjects in each treatment arm. However, biased coin designs necessitate subjects being randomized with different treatment probabilities and a given subject’s treatment probability depending on the treatment assignment of everyone who preceded them in a complex way. The matched randomization design, such as that proposed in Greevy, Silber, and Rosenbaum’s 2004 Biostatistics paper, has the benefit of each subject being randomized with probability 0.5 in a two-arm trial and a simple dependence structure for the treatment assignments. This talk adapts the matched randomization method of Greevy, Silber, and Rosenbaum to randomized controlled trials where subjects trickle in one at a time or in small batches. The proposed method employs optimal nonbipartite matching with a reweighted Mahalanobis distance, or a weighted Euclidean distance, and the use of flexible near-matchers.