A new proposal for setting parameter values in restricted randomization methods

Complete randomization could result in an undesirable imbalance in the number of patients assigned to each treatment, especially in small trials. Therefore, a variety of restricted randomization procedures has been developed. By varying parameters it is possible to appropriately modify the balancing characteristics of these designs. However, there is little information on what are sensible choices for the parameters. Therefore, we suggest a new method for suitable determination of parameter values of restricted randomization rules.

For restriction to be effective, it need not yield exact equality. As the reliability of a test is not very sensitive to slight deviations from equal sample sizes we define that a given maximum tolerable imbalance d can be achieved or exceeded with a given probability p(*). By using this condition, parameter values of restricted procedures are determinable.

For permuted-block, biased-coin, urn, and big-stick randomization we investigated the impact of parameters on balancing properties. For different extents of restriction and by using the submitted condition, the values of parameters to be chosen are determined.

Up to now choice of parameter values has often occurred at random. Now it is possible to determine values of parameters by specifying the tolerable degree of imbalance and the risk to be worse. As a consequence restriction will, as much as possible, not be imposed and not imposed more than necessary in order to preserve the intrinsic quality of randomization.