Hu, Yanqing; Hu, Feifang Asymptotic properties of covariate-adaptive randomization. (English) Zbl 1257.62104 Ann. Stat. 40, No. 3, 1794-1815 (2012). Summary: 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 [S.J. Pocock and R. Simon, Biometrics 31, 103–115 (1975)] 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. 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. Cited in 41 Documents MSC: 62P10 Applications of statistics to biology and medical sciences; meta analysis 60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) 92C50 Medical applications (general) 65C60 Computational problems in statistics (MSC2010) Keywords:balancing covariates; clinical trials; marginal balance; Markov chains; Pocock and Simon design; stratified permuted blocks × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid References: [1] Atkinson, A. C. (1982). Optimum biased coin designs for sequential clinical trials with prognostic factors. Biometrika 69 61-67. · Zbl 0483.62067 · doi:10.1093/biomet/69.1.61 [2] Bai, Z. D. and Hu, F. (1999). Asymptotic theorems for urn models with nonhomogeneous generating matrices. Stochastic Process. Appl. 80 87-101. · Zbl 0954.62014 · doi:10.1016/S0304-4149(98)00094-5 [3] Begg, C. B. and Iglewicz, B. (1980). 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