Revisiting Randomization with the Cube Method

Abstract: We propose a novel randomization approach for randomized controlled trials (RCTs), based on the cube method developed by Deville and Till\'e (2004). The cube method allows for the selection of balanced samples across various covariate types, ensuring consistent adherence to balance tests and, whence, substantial precision gains when estimating treatment effects. We establish several statistical properties for the population and sample average treatment effects under randomization using the cube method. We formally derive and compare bounds on imbalances depending on the number of units $n$ and the number of covariates $p$ considered for the balancing. We show that our randomization approach outperforms methods proposed in the literature when $p$ is large and $p/n$ tends to 0. We run simulation studies to illustrate the substantial gains from the cube method for a large set of covariates.