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Baseline covariates are routinely used at both the design and analysis stages of RCTs. At the design stage, covariate adjustment is mainly through covariate-adaptive randomization (e.g., stratified permuted block randomization), which gains credibility but poses challenge to the downstream analysis as treatment assignment is no longer independent. At the analysis stage, the method used for covariate adjustment should provide ``valid inference under approximately the same minimal statistical assumptions that would be needed for unadjusted estimation’’, and ideally guarantee efficiency gain over the unadjusted estimation.
In this talk, we discuss how covariate adjustment at the two different stages affects the inference of treatment effect. Besides robustness and efficiency, we argue that universality – a valid inference procedure can be universally applicable to all commonly used randomization schemes – is another key aspect in evaluating analysis methods. We present comprehensive results for continuous, discrete, and time-to-event outcomes in terms of these three aspects under ``minimal statistical assumptions.’’ Our results also reveal the duality between design and analysis, and provide important guidance for the practice.