2020/04/06 by Feifang Hu, Zhang Li, Hu, Feifang +1
Decision Sciences · Mathematics · #60F15 #62G10 #Advanced Statistical Process Monitoring #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Optimal Experimental Design Methods #Statistical Methods in Clinical Trials #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2004.02994
openalex publication_date 2020/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Pocock and Simon's marginal procedure (Pocock and Simon, 1975) is often implemented forbalancing treatment allocation over influential covariates in clinical trials. However, the theoretical properties of Pocock and Simion's procedure have remained largely elusive for decades. In this paper, we propose a general framework for covariate-adaptive designs and establish the corresponding theory under widely satisfied conditions. As a special case, we obtain the theoretical properties of Pocock and Simon's marginal procedure: the marginal imbalances and overall imbalance are bounded in probability, but the within-stratum imbalances increase with the rate of √(n) as the sample size increases. The theoretical results provide new insights about balance properties of covariate-adaptive randomization procedures and open a door to study the theoretical properties of statistical inference for clinical trials based on covariate-adaptive randomization procedures.