Asymptotic properties of covariate-adaptive randomization

TL;DR

This paper introduces a new covariate-adaptive randomization method for clinical trials that improves balance across multiple covariates and provides a theoretical foundation for its properties.

Contribution

It proposes a novel covariate-adaptive design that controls imbalances and establishes its theoretical properties using Markov chain analysis.

Findings

The joint process of imbalances is a positive recurrent Markov chain.

The new method achieves better overall balance than traditional approaches.

Simulation studies confirm the effectiveness of the proposed design.

Abstract

Balancing treatment allocation for influential covariates is critical in clinical trials. This has become increasingly important as more and more biomarkers are found to be associated with different diseases in translational research (genomics, proteomics and metabolomics). Stratified permuted block randomization and minimization methods [Pocock and Simon Biometrics 31 (1975) 103-115, etc.] are the two most popular approaches in practice. However, stratified permuted block randomization fails to achieve good overall balance when the number of strata is large, whereas traditional minimization methods also suffer from the potential drawback of large within-stratum imbalances. Moreover, the theoretical bases of minimization methods remain largely elusive. In this paper, we propose a new covariate-adaptive design that is able to control various types of imbalances. We show that the joint process of within-stratum imbalances is a positive recurrent Markov chain under certain conditions. Therefore, this new procedure yields more balanced allocation. The advantages of the proposed procedure are also demonstrated by extensive simulation studies. Our work provides a theoretical tool for future research in this area.