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Inference after covariate-adaptive randomisation: aspects of methodology and theory

Covariate-adaptive randomisation has a more than 45 years of history of applications in clinical trials, in order to balance treatment assignments across prognostic factors that may have influence on the outcomes of interest. However, almost no theory had been developed for covariate-adaptive randomisation until a paper on the theory of testing hypotheses published in 2010. In this article, we review aspects of methodology and theory developed in the last decade for statistical inference under covariate-adaptive randomisation. We focus on issues such as whether a conventional procedure valid under the assumption that treatments are assigned completely at random is still valid or conservative when the actual randomisation is covariate-adaptive, how a valid inference procedure can be obtained by modifying a conventional method or directly constructed by stratifying the covariates used in randomisation, whether inference procedures have different properties when covariate-adaptive randomisation schemes have different degrees of balancing assignments, and how to further adjust covariates in the inference procedures to gain more efficiency. Recommendations are made during the review and further research problems are discussed.