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 imbalanced observed covariates, increasing estimator error. There is also imbalance on unobserved covariates which likewise increase estimator error. Rerandomization can throw away poor assignments only in the observed covariates by limiting the imbalance to a prespecified threshold. Limiting this threshold too much can increase the risk of having error due to unobserved covariates. We introduce a criterion that gauges errors due to both imbalance in the observed and the risk of imbalance in the unobserved covariates. We then use this criterion to locate the optimal rerandomization threshold based on the practitioner's level of desired insurance. We also provide an open source R package available on CRAN named OptimalRerandExpDesigns which generates designs according to our algorithm.