A Comparison of Randomization Methods for Multi-Arm Clinical Trials

Randomized controlled trials are widely accepted as the best design for evaluating the efficacy of a treatment, due to the advantages of randomization. The objectives of randomization include removing bias in the assignment of treatments, balancing numbers allocated to arms, and balancing observed and unobserved covariates between arms. Different randomization procedures, each with varying properties of randomness and balance, are available and investigators must be careful to select one that will result in desirable properties. In this article, we use a simulation study, based on two real clinical trials, to empirically test several allocation procedures for multi-arm trials: simple randomization, permuted block randomization, stratified randomization with permuted blocks, urn design, block urn design, stratified block urn design, and minimization. We evaluate properties such as group size balance, covariate balance, loss of precision (i.e., increase in the variance of treatment effect estimates), and predictability of assignment. We also compare different definitions of statistical power relevant in multi-arm trials: marginal, disjunctive, and conjunctive powers. Based on the simulation results, the considered randomization methods have very little impact on the resultant powers. Consistently strong performance was seen across the performance metrics for stratified block randomization and the stratified block urn design.