PCA Rerandomization

Mahalanobis distance of covariate means between treatment and control groups is often adopted as a balance criterion when implementing a rerandomization strategy. However, this criterion may not work well for high-dimensional cases because it balances all orthogonalized covariates equally. We propose using principal component analysis (PCA) to identify proper subspaces in which Mahalanobis distance should be calculated. Not only can PCA effectively reduce the dimensionality for high-dimensional covariates, but it also provides computational simplicity by focusing on the top orthogonal components. The PCA rerandomization scheme has desirable theoretical properties for balancing covariates and thereby improving the estimation of average treatment effects. This conclusion is supported by numerical studies using both simulated and real examples.

Automated summary

The Mahalanobis distance of covariate means is commonly used to achieve balance in rerandomization strategies. However, this criterion might not work well for high-dimensional cases as it treats all orthogonalized covariates equally. To address this issue, we propose using PCA to identify relevant subspaces for calculating Mahalanobis distance. PCA not only reduces dimensionality but also simplifies computation by focusing on the top orthogonal components. Our PCA rerandomization approach improves covariate balance and enhances the estimation of average treatment effects, as demonstrated in numerical studies with simulated and real data.