Properties of restricted randomization with implications for experimental design
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Recently, there as been an increasing interest in the use of heavily restricted randomization designs which enforces balance on observed covariates in randomized controlled trials. However, when restrictions are too strict, there is a risk that the treatment effect estimator will have a very high mean squared error. In this paper, we formalize this risk and propose a novel combinatoric-based approach to describe and address this issue. First, some known properties of complete randomization and restricted randomization are re-proven using basic combinatorics. Second, a novel diagnostic measure that only use the information embedded in the combinatorics of the design is proposed. Finally, we identify situations in which restricted designs can lead to an increased risk of getting a high mean squared error and discuss how our diagnostic measure can be used to detect and avoid such designs. Our results have implications for any restricted randomization design and can be used to evaluate the trade-off between enforcing balance on observed covariates and avoiding too restrictive designs.
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