Multi-arm covariate-adaptive randomization

Abstract

Simultaneously investigating multiple treatments in a single study achieves considerable efficiency in contrast to the traditional two-arm trials. Balancing treatment allocation for influential covariates has become increasingly important in today's clinical trials. The multi-arm covariate-adaptive randomized clinical trial is one of the most powerful tools to incorporate covariate information and multiple treatments in a single study.Pocock and Simon's procedure has been extended to the multi-arm case. However, the theoretical properties of multi-arm covariate-adaptive randomization have remained largely elusive for decades. In this paper, we propose a general framework for multi-arm covariate-adaptive designs which also includes the two-arm case, and establish the corresponding theory under widely satisfied conditions. The theoretical results provide new insights about balance properties of covariate-adaptive randomization procedures and make foundations for most existing statistical inferences under two-arm covariate-adaptive randomization. Furthermore, these open a door to study the theoretical properties of statistical inferences for clinical trials based on multi-arm covariate-adaptive randomization procedures.

Regression analysis for covariate‐adaptive randomization: A robust and efficient inference perspective

“…In the latter case of $$$ {q}_{\left[k\right]}=0 $$$, we say that the randomization achieves strong balance 15 . Moreover, Assumption 4 is weaker than Assumption 3 as no (asymptotic) independence is required between different strata, and it allows us to consider covariate‐adaptive randomization that pursues balance within covariate margins and thus has a complicated dependence structure across strata, such as minimization 5,7 and the class of designs proposed by Hu and Hu 6 . We emphasize that while Assumption 3 applies primarily to stratified randomization, Assumption 4 is quite general and is satisfied by most covariate‐adaptive randomization methods encountered in practice.…”

“…Pocock and Simon proposed a minimization procedure, which we refer to simply as minimization in this article, to achieve balance over covariates' margins 5 . This approach has been generalized for use in simultaneously controlling various types of imbalances (within‐stratum, within‐covariate‐margin, and overall) 6,7 . For a more comprehensive review, see Rosenberger 8 .…”

“…5 This approach has been generalized for use in simultaneously controlling various types of imbalances (within-stratum, within-covariate-margin, and overall). 6,7 For a more comprehensive review, see Rosenberger. 8 The use of covariate-adaptive randomization predominates in clinical trials.…”

Regression-Based Multiple Treatment Effect Estimation under Covariate-Adaptive Randomization

“…Several well‐known randomization schemes satisfy this assumption, such as simple randomization, stratified permuted block randomization (Zelen, 1974) and stratified biased coin randomization (Kuznetsova & Johnson, 2017; Shao et al., 2010). In the special case in which $$\pi _{[k]a}$$ are identical across all strata for each treatment group, Pocock and Simon's minimization (Pocock & Simon, 1975) also satisfies this assumption (Hu et al., 2023).…”

“…Minimization (Pocock & Simon, 1975; Taves, 1974) has been used for balancing covariates over their margins. This scheme has been generalized to control other types of imbalance measures, which may include overall and within‐stratum imbalance measures (Hu & Hu, 2012; Hu et al., 2023). Details of above randomization methods and other methods such as stratified biased coin design (Efron, 1971; Shao et al., 2010) and model‐based approaches (Atkinson, 1982; Begg & Iglewicz, 1980) are described in Rosenberger and Lachin (2015).…”