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Covariate-adaptive randomization schemes such as the minimization andstratified permuted blocks are often applied in clinical trials to balancetreatment assignments across prognostic factors. The existing theoreticaldevelopments on inference after covariate-adaptive randomization are mostlylimited to situations where a correct model between the response and covariatescan be specified or the randomization method has well-understood properties.Based on stratification with covariate levels utilized in randomization and afurther adjusting for covariates not used in randomization, in this article wepropose several estimators for model free inference on average treatment effectdefined as the difference between response means under two treatments. Weestablish asymptotic normality of the proposed estimators under all popularcovariate-adaptive randomization schemes including the minimization whosetheoretical property is unclear, and we show that the asymptotic distributionsare invariant with respect to covariate-adaptive randomization methods.Consistent variance estimators are constructed for asymptotic inference.Asymptotic relative efficiencies and finite sample properties of estimators arealso studied. We recommend using one of our proposed estimators for valid andmodel free inference after covariate-adaptive randomization.

Inference on Average Treatment Effect under Minimization and Other Covariate-Adaptive Randomization Methods