Covariate-adaptive randomization is widely employed to balance baseline covariates in interventional studies such as clinical trials and experiments in development economics. Recent years have witnessed substantial progress in inference under covariate-adaptive randomization with a fixed number of strata. However, concerns have been raised about the impact of a large number of strata on its design and analysis, which is a common scenario in practice, such as in multicenter randomized clinical trials. In this paper, we propose a general framework for inference under covariate-adaptive randomization, which extends the seminal works of Bugni et al. (2018, 2019) by allowing for a diverging number of strata. Furthermore, we introduce a novel weighted regression adjustment that ensures efficiency improvement. On top of establishing the asymptotic theory, practical algorithms for handling situations involving an extremely large number of strata are also developed. Moreover, by linking design balance and inference robustness, we highlight the advantages of stratified block randomization, which enforces better covariate balance within strata compared to simple randomization. This paper offers a comprehensive landscape of inference under covariate-adaptive randomization, spanning from fixed to diverging to extremely large numbers of strata.

翻译：协变量自适应随机化被广泛应用于干预性研究（如临床试验和发展经济学实验）中以平衡基线协变量。近年来，在固定分层数目的协变量自适应随机化下的推断研究取得了实质性进展。然而，实践中常见的大规模分层情形（如多中心随机临床试验）对其设计与分析的影响引发了广泛关注。本文提出了一个协变量自适应随机化下推断的通用框架，该框架通过允许分层数目发散，拓展了Bugni等人（2018, 2019）的开创性工作。此外，我们引入了一种新型加权回归调整方法以确保效率提升。在建立渐近理论的基础上，本文还开发了处理极端大规模分层情形的实用算法。通过关联设计平衡性与推断稳健性，我们强调了分层区组随机化的优势——相较于简单随机化，该方法能在各层内实现更好的协变量平衡。本文系统阐述了从固定分层数目到发散分层数目，再到极端大规模分层数目下协变量自适应随机化的推断理论，为该领域提供了完整的理论图景。