Improved estimation of average treatment effects under covariate‐adaptive randomization methods

Estimation of the average treatment effect is one of the crucial problems in clinical trials for two or multiple treatments. The covariate‐adaptive randomization methods are often applied to balance treatment assignments across prognostic factors in clinical trials, such as the minimization and stratified permuted blocks method. We propose a model‐free estimator of average treatment effects under covariate‐adaptive randomization methods, which is least square adjustment for the estimator of outcome models. The proposed estimator is not only applicable to the case of binary treatment, but also can be extended to the case of multiple treatment. The proposed estimator is consistent and asymptotically normally distributed. Simulation studies show that the proposed estimator and Ye's estimator are comparable, and it performs better than Bugni's estimator when the outcome model is linear. The proposed estimator has some advantages over targeted maximum likelihood estimator, Bugni's estimator and Ye's estimator in terms of the standard error and root mean squared error when the outcome model is nonlinear. The proposed estimator is stable for the from of outcome model. Finally, we apply the proposed methodology to a dataset that studies the causal effect promotional videos mode on the school‐age children's educational attainment in Peru.