  Covariate-adaptive randomization schemes such as the minimization and
stratified permuted blocks are often applied in clinical trials to balance
treatment assignments across prognostic factors. The existing theoretical
developments on inference after covariate-adaptive randomization are 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 adjusting for covariates not used in randomization, in this article we
propose several estimators for model free inference on average treatment effect
defined as the difference between response means under two treatments. We
establish asymptotic normality of the proposed estimators under all popular
covariate-adaptive randomization schemes including the minimization whose
theoretical property is unclear, 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.
