Blocking, rerandomization, and regression adjustment in randomized experiments with high-dimensional covariates

Blocking, a special case of rerandomization, is routinely implemented in the design stage of randomized experiments to balance baseline covariates. Regression adjustment is highly encouraged in the analysis stage to adjust for the remaining covariate imbalances. Researchers have recommended combining these techniques; however, the research on this combination in a randomization-based inference framework with a large number of covariates is limited. This paper proposes several methods that combine the blocking, rerandomization, and regression adjustment techniques in randomized experiments with high-dimensional covariates. In the design stage, we suggest the implementation of blocking or rerandomization or both techniques to balance a fixed number of covariates most relevant to the outcomes. For the analysis stage, we propose regression adjustment methods based on the Lasso to adjust for the remaining imbalances in the additional high-dimensional covariates. Moreover, we establish the asymptotic properties of the proposed Lasso-adjusted average treatment effect estimators and outline conditions under which these estimators are more efficient than the unadjusted estimators. In addition, we provide conservative variance estimators to facilitate valid inferences. Our analysis is randomization-based, allowing the outcome data generating models to be mis-specified. Simulation studies and two real data analyses demonstrate the advantages of the proposed methods.