A unifying framework for standard and covariate-adaptive randomization procedures based on minimizing suitable imbalance functions

Minimization is based on minimizing an imbalance function defined in terms of one or more covariates. Standard (non-adaptive) randomization procedures, on the other hand, generally do not specify or try to minimize an imbalance function. However, it turns out that they may be formulated in this manner. Doing so places adaptive and standard randomization procedures within the same framework, and also suggests novel randomization procedures that combine the best elements of both.