Randomization by minimization for unbalanced treatment allocation

Abstract

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.

A Randomized Controlled Trial Evaluating the Efficacy of a Psychoeducation Program for Families of Children and Adolescents With ADHD in the United Kingdom: Results After a 6-Month Follow-Up

“…Randomization by minimization was applied, including gender, age, and medication use as factors (Han, Enas, & McEntegart, 2009). Randomization was performed using a computerized program (MACRO™) provided by the Clinical Trials Unit at King's College, London, once families gave their consent.…”

Issues for stratified randomization based on a factor derived from a continuous baseline variable

“…For example, randomization by minimization has been proposed by Taves [15]. Some recent advances in this area can be found in references [16,17].…”

Sequence balance minimisation: minimising with unequal treatment allocations

“…The chosen treatment could simply be taken as the one with the lower score or a random element could be introduced [1]. It is customary to introduce a random element to make the allocations more unpredictable [5]; the preferred treatment is assigned with a higher allocation probability, and non-preferred treatments are given low probabilities [5, 6]. In practise, one has to select that p (i.e., allocation probability) which strikes a balance between minimising treatment imbalance and avoiding predictability of treatment assignment [5].…”

“…Han et al [6] showed that the minimisation process needs to be modified for trials involving unbalanced or unequal treatment allocations. Authors introduced two modifications.…”

“…Once the preferred treatment is determined, probability assignment would proceed as for the minimisation process for equal treatment allocations. Han et al [6] showed, however, that this simple modification can lead to deviations from the target allocation ratio, especially when the allocation probability given to the preferred treatment is relatively low. To avoid this problem, they proposed to account for unequal allocation ratios in determining allocation probabilities.…”