Abstract
Rerandomization is a strategy for improving balance on observed covariates in randomized controlled trials. It has been both advocated and advised against by renowned scholars of experimental design. However, the relationship and differences between stratification, rerandomization, and the combination of the two have not been previously investigated. In this paper, we show that stratified designs can be recreated by rerandomization and explain why, in most cases, stratification on binary covariates followed by rerandomization on continuous covariates is more efficient than rerandomization on all covariates at the same time.
Highlights
The most common design used to improve balance in a randomized control trials is stratified randomization, which is called blocked randomization
The Monte Carlo simulations show that the theoretical findings apply in finite sample settings and indicate that they are robust to violations of the normality assumption of the covariate means and error term
In such situations, stratified rerandomization is a good strategy for reducing the number of degrees of freedom in the Chi-square distribution of the Mahalanobis distance
Summary
The most common design used to improve balance in a randomized control trials is stratified randomization, which is called blocked randomization. Units from all strata are represented in both the treatment and control groups and imbalances on any of these covariates are thereby avoided, see e.g. Imbens and Rubin (2015) for a recent overview The motivation for rerandomization is based on an understanding of that, after blocking, complete randomization within strata can result in imbalances in other covariates In this situation, Fisher is alleged to have recommended rerandomization (Morgan and Rubin, 2012). In The Handbook of Economic Field Experiments, Athey and Imbens (2016) recommended researchers to first and foremost take care in the ‘original design’ to rule out unbalanced assignments instead of relying on rerandomization This recommendation by the authors may be interpreted that they view rerandomization as a substitute for stratification which may be unfortunate if relevant continuous covariates are available.
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