Bootstrapping inference of average treatment effect in completely randomized experiments with high-dimensional covariates

Investigators often use regression adjustment methods to analyze the results of randomized experiments when baseline covariates are available. Their aim is to improve the estimation efficiency of treatment effects by adjusting for imbalance of covariates. Under mild conditions, the regression-adjusted average treatment effect estimator is asymptotically normal with asymptotic variance no greater than that of the unadjusted estimator. The asymptotic variance can be estimated conservatively based on residual sum of squares. This article studies alternative inference methods based on the bootstrap and investigates their asymptotic properties under the Neyman–Rubin causal model and randomization-based inference framework. We show that the weighted, residual and paired bootstrap methods provide asymptotically conservative variance estimators that perform at least as good as the estimator based on residual sum of squares. We further provide counterexamples, where the original estimator is asymptotically normal, but the bootstrap counterpart is inconsistent for estimating its limiting distribution. Simulation studies indicate that the paired bootstrap method is preferable, in terms of preserving type I errors, for a small sample size. Finally, our methods analyze HER2+ breast cancer data from the NeOAdjuvant Herceptin trial to examine the effectiveness of trastuzumab in combination with neoadjuvant chemotherapy.