Randomization by minimization for unbalanced treatment allocation.

Minimization is a dynamic randomization technique that has been widely used in clinical trials for achieving a balance of prognostic factors across treatment groups, but most often it has been used in the setting of equal treatment allocations. Although unequal treatment allocation is frequently encountered in clinical trials, an appropriate minimization procedure for such trials has not been published. The purpose of this paper is to present novel strategies for applying minimization methodology to such clinical trials. Two minimization techniques are proposed and compared by probability calculation and simulation studies. In the first method, called naïve minimization, probability assignment is based on a simple modification of the original minimization algorithm, which does not account for unequal allocation ratios. In the second method, called biased-coin minimization (BCM), probability assignment is based on allocation ratios and optimized to achieve an 'unbiased' target allocation ratio. The performance of the two methods is investigated in various trial settings including different number of treatments, prognostic factors and sample sizes. The relative merits of the different distance metrics are also explored. On the basis of the results, we conclude that BCM is the preferable method for randomization in clinical trials involving unequal treatment allocations. The choice of different distance metrics slightly affects the performance of the minimization and may be optimized according to the specific feature of trials.