Algorithms for minimization randomization and the implementation with an R package

Randomization is an established process to assign participants to treatment groups to reduce selection bias. Minimization is a method of dynamic or adaptive randomization to minimize the imbalance between treatment groups with respect to the number of participants over the participant's predefined covariate factors. The algorithms for minimization randomization with equal allocation ratio have been well studied in the literature. With the growing demand for unequal allocation in clinical trials, an allocation ratio preserving biased coin minimization (ARP BCM) was proposed to preserve the allocation ratio at every allocation step, using measure of imbalance by the range. In this article, we expand the ARP BCM to unequal allocation which preserves the allocation ratio at every allocation, using more measures of imbalance by the standard deviation and variance. Simulations have been conducted to evaluate the performance of these methods. Furthermore, these algorithms have been implemented in a newly developed R package 'Minirand'.