Randomization inference for balanced cluster-randomized trials

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Abstract
This paper discusses the choice of randomization tests for inferences from cluster-randomized trials that have been designed to ensure a balanced allocation of clusters to treatments. Methods for covariate-adjusted randomization tests are reviewed and their application to balanced cluster-randomized trials discussed. Two cluster-randomized trials with balanced designs are used to illustrate the choices that can be made in selecting a randomization test, and methods for obtaining confidence intervals for treatment effects are illustrated. The balance imposed by the randomization in these trials makes adjustment for covariates less beneficial than for an unbalanced design. However, the adjusted analyses do not appear generally to have worse properties than the unadjusted ones, and may provide protection against any imbalance that has not been controlled for in the design. The only case when adjustment for covariates may result in worse precision is when a large number of cluster-level covariates are included in the analysis. An expression is provided that allows the size of this effect to be calculated for any given set of cluster-level covariates.