• BMW design;
  • Clustered randomized trial;
  • Experimental design;
  • Optimal matching;
  • Propensity score matching;
  • Randomization tests;
  • Repeated randomization


Cluster randomized trials with relatively few clusters have been widely used in recent years for evaluation of health-care strategies. The balance match weighted (BMW) design, introduced in Xu and Kalbfleisch (2010, Biometrics 66, 813–823), applies the optimal full matching with constraints technique to a prospective randomized design with the aim of minimizing the mean squared error (MSE) of the treatment effect estimator. This is accomplished through consideration of M independent randomizations of the experimental units and then selecting the one which provides the most balance evaluated by matching on the estimated propensity scores. Often in practice, clinical trials may involve more than two treatment arms and multiple treatment options need to be evaluated. Therefore, we consider extensions of the BMW propensity score matching method to allow for studies with three or more arms. In this article, we propose three approaches to extend the BMW design to clinical trials with more than two arms and evaluate the property of the extended design in simulation studies.