The properties of covariate-adaptive randomization procedures with possibly unequal allocation ratio
The Annals of Applied Statistics · 2025 · Volume 19 · Issue 2
Abstract
In clinical trials, covariate-adaptive randomization (CAR) procedures are used to balance important covariates for more convincing results and enhanced statistical efficiency. Although most CAR procedures focus on trials with 1:1 allocation ratio, the demand for unequal allocation is growing. Therefore, this paper proposes a CAR framework that unifies numerous existing procedures and can balance general (discrete, continuous, or their combinations) covariates under any allocation ratio. To evaluate the proposed procedure, we classify covariates into randomized covariates and additional covariates, based on whether or not they are used in the randomization procedure. The analysis indicates that our proposed procedure possesses superior balancing properties for randomized covariates. Subsequently, we investigate the impact of CAR procedures on additional covariates. When balancing only discrete covariates, our results exhibit the benefit of CAR procedures in balancing additional covariates. However, the most intriguing finding is that, under unequal allocation ratio, balancing continuous covariates will challenge the balance of additional covariates, and we refer to this new issue as the “shift problem.” To understand and remedy this issue, we perform a comprehensive analysis about when and why it occurs, followed by two practical solutions to address the shift problem. The proposed CAR procedures are shown to effectively balance covariates when applied to the data from a depression trial.
Keywords
balancing additional covariates, covariate balance, covariate-adaptive randomization, shift problem, unequal allocation ratio
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