Optimal Rerandomization via a Criterion that Provides Insurance Against Failed Experiments

We present an optimized rerandomization design procedure for a non-sequential treatment-control experiment. Randomized experiments are the gold standard for finding causal effects in nature. But sometimes random assignments result in unequal partitions of the treatment and control group visibly seen as imbalance in observed covariates. There can additionally be imbalance on unobserved covariates. Imbalance in either observed or unobserved covariates increases treatment effect estimator error inflating the width of confidence regions and reducing experimental power. "Rerandomization" is a strategy that omits poor imbalance assignments by limiting imbalance in the observed covariates to a prespecified threshold. However, limiting this threshold too much can increase the risk of contracting error from unobserved covariates. We introduce a criterion that combines observed imbalance while factoring in the risk of inadvertently imbalancing unobserved covariates. We then use this criterion to locate the optimal rerandomization threshold based on the practitioner's level of desired insurance against high estimator error. We demonstrate the gains of our designs in simulation and in a dataset from a large randomized experiment in education. We provide an open source R package available on CRAN named OptimalRerandExpDesigns which generates designs according to our algorithm.
Comment: 27 pages, 5 figures, 2 tables, 2 algorithms