Statistical properties of minimal sufficient balance and minimization as methods for controlling baseline covariate imbalance at the design stage of sequential clinical trials

Abstract

When the number of baseline covariates whose imbalance needs to be controlled in a sequential randomized controlled trial is large, minimization is the most commonly used method for randomizing treatment assignments. The lack of allocation randomness associated with the minimization method has been the source of controversy, and the need to reduce even minor imbalances inherent in the minimization method has been challenged. The minimal sufficient balance (MSB) method is an alternative to the minimization method. It prevents serious imbalance from a large number of covariates while maintaining a high level of allocation randomness. In this study, the two treatment allocation methods are compared with regards to the effectiveness of balancing covariates across treatment arms and allocation randomness in equal allocation clinical trials. The MSB method proves to be equal or superior in both respects. In addition, type I error rate is preserved in analyses for both balancing methods, when using a binary endpoint.

Impact of minimal sufficient balance, minimization, and stratified permuted blocks on bias and power in the estimation of treatment effect in sequential clinical trials with a binary endpoint

“…MSB allows complete randomization to take place for a majority of subjects that are assigned to a treatment arm. A biased coin is only used when a serious imbalance is present, which, as we found in Lauzon et al 13 is substantially less often than in minimization. Moreover, when p-values are used to determine serious imbalances, smaller absolute differences are permitted as sample size increases, whereas minimization attempts to control minor imbalances regardless of sample size.…”

“…Allocation randomness remains the most important argument for use of MSB in clinical trials because completely random treatment assignments protects against imbalance of known and unknown covariates and is the basis for inference. 13…”

“…Allocation randomness remains the most important argument for use of MSB in clinical trials because completely random treatment assignments protects against imbalance of known and unknown covariates and is the basis for inference. 13 Further research should explore each method in a variety of modeling situations and with different types of outcomes, including continuous outcomes and time-to-event outcomes. Additionally, it should be noted that small differences in power (such as 1-2%) may be statistically significant while not being clinically meaningful in a specific study.…”

“…For simplicity, only randomization in sequential clinical trials consisting of a treatment with two levels, equal marginal allocation ratios for each treatment, and a binary outcome are considered. More complex modeling, such as a model with five and 11 covariates, has been considered in Lauzon et al 13 The five methods of randomization considered are complete randomization, stratified permuted blocks, minimization with biased coin treatment assignments (referred to as minimization), minimization with deterministic treatment assignments (referred to as deterministic minimization), and MS. In this study, the stratified permuted block method uses a block size of six, which is arbitrarily chosen without loss of generality.…”

Common scale minimal sufficient balance: An improved method for covariate‐adaptive randomization based on the Wilcoxon‐Mann‐Whitney odds ratio statistic

“…Simulation studies of MSB 10 have demonstrated that the method successfully controls covariate imbalance when the number of covariates is large, and does not adversely impact Type‐I error. MSB been used to control covariate balance in stroke, 11 , 12 , 13 Parkinson's Disease 14 and postsurgical physiotherapy.…”