Theoretical Properties of Covariate-Adaptive Randomization with a Diverging Number of Covariates

2026-08-13

AI Summary

This study addresses the lack of theoretical justification for covariate-adaptive randomization in high-dimensional settings where the number of covariates grows with the sample size. The authors develop a unified theoretical framework to analyze the imbalance properties of two classes of adaptive randomization procedures, both for specified and unspecified covariates. Leveraging high-dimensional probabilistic limit theory and imbalance analysis, they establish—for the first time—the convergence rates of covariate imbalance under this asymptotic regime and prove the asymptotic normality of the average treatment effect estimator. Furthermore, they derive valid confidence intervals based on these results. Numerical experiments corroborate the practical relevance of the theoretical findings, thereby providing a rigorous statistical foundation for high-dimensional causal inference.

Abstract

Covariate-adaptive randomization procedures are widely used in clinical trials to improve covariate balance. In modern applications, experimenters often have access to many covariates, motivating the need for a theory of covariate-adaptive randomization procedures with a diverging number of covariates. In this paper, we study the theoretical properties of two unified families of covariate-adaptive randomization procedures under high-dimensional settings. For the two procedures, we establish the convergence rate of the imbalance measure corresponding to the specified covariates. In addition, for one of them, we study the asymptotic properties of the imbalance of unspecified covariates under and apply these results to derive the asymptotic properties of the difference-in-means estimator for the average treatment effect and construct asymptotic 95% confidence intervals. Furthermore, we provide extensive numerical and empirical studies to illustrate the practical relevance of our theoretical results.

Problem

• covariate-adaptive randomization
• diverging covariates
• high-dimensional settings
• covariate balance
• clinical trials

Innovation

• covariate-adaptive randomization
• diverging covariates
• high-dimensional asymptotics
• imbalance measure
• average treatment effect