Multi-arm randomization has increasingly widespread applications recently and it is also crucial to ensure that the distributions of important observed covariates as well as the potential unobserved covariates are similar and comparable among all the treatment. However, the theoretical properties of unobserved covariates imbalance in multi-arm randomization with unequal allocation ratio remains unknown. In this paper, we give a general framework analysing the moments and distributions of unobserved covariates imbalance and apply them into different procedures including complete randomization (CR), stratified permuted block (STR-PB) and covariate-adaptive randomization (CAR). The general procedures of multi-arm STR-PB and CAR with unequal allocation ratio are also proposed. In addition, we introduce the concept of entropy to measure the correlation between discrete covariates and verify that we could utilize the correlation to select observed covariates to help better balance the unobserved covariates.

翻译：近年来，多臂随机化的应用日益广泛，确保所有处理组间重要观测协变量及潜在未观测协变量的分布相似且可比至关重要。然而，不等分配比多臂随机化中未观测协变量失衡的理论性质尚未明确。本文提出一个分析未观测协变量失衡矩与分布的通用框架，并将其应用于完全随机化（CR）、分层置换区组（STR-PB）和协变量自适应随机化（CAR）等不同流程。同时提出了不等分配比多臂STR-PB与CAR的通用实施流程。此外，我们引入熵的概念来衡量离散协变量间的相关性，并通过验证表明可利用这种相关性选择观测协变量，以促进未观测协变量达到更优平衡。