Inference on the average treatment effect under minimization and other covariate-adaptive randomization methods

Summary Covariate-adaptive randomization schemes such as minimization and stratified permuted blocks are often applied in clinical trials to balance treatment assignments across prognostic factors. The existing theory for inference after covariate-adaptive randomization is mostly limited to situations where a correct model between the response and covariates can be specified or the randomization method has well-understood properties. Based on stratification with covariate levels utilized in randomization and a further adjustment for covariates not used in randomization, we propose several model-free estimators of the average treatment effect. We establish the asymptotic normality of the proposed estimators under all popular covariate-adaptive randomization schemes, including the minimization method, and we show that the asymptotic distributions are 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 are also studied. We recommend using one of our proposed estimators for valid and model-free inference after covariate-adaptive randomization.