Dynamic balancing randomization in controlled clinical trials.

In the design of randomized clinical trials, balancing of treatment allocation across important prognostic factors (strata) improves the efficiency of the final comparisons. Whilst randomization methods exist which attempt to balance treatments across the strata (permuted blocks, minimization, biased coin), these approaches assign equal importance for all the strata. Dynamic balancing randomization (DBR) is a tree-based method proposed by Signorini et al. allowing different levels of imbalance in different strata which ensures a balance for each level of prognostic risk factors (conditional balance) whilst at the same time preserving randomness. We present a simple modification to the original approach to maintain a marginal balance over important strata and examine the properties of this modification. Two important measures of performance are used to provide comparisons between the approaches: a loss function, which can be interpreted as the squared norm of the imbalance vector, and a forcing index which conveys the degree of randomness. A comparison of DBR with minimization and a biased coin design is carried out by simulation on two simulated trials.