Cvcrand and Cptest: Commands for Efficient Design and Analysis of Cluster Randomized Trials Using Constrained Randomization and Permutation Tests

Cluster randomized trials (CRTs), where clusters (for example, schools or clinics) are randomized to comparison arms but measurements are taken on individuals, are commonly used to evaluate interventions in public health, education, and the social sciences. Because CRTs typically involve a small number of clusters (for example, fewer than 20), simple randomization frequently leads to baseline imbalance of cluster characteristics across study arms, threatening the internal validity of the trial. In CRTs with a small number of clusters, classic approaches to balancing baseline characteristics—such as matching and stratification—have several drawbacks, especially when the number of baseline characteristics the researcher desires to balance is large (Ivers et al., 2012, Trials 13: 120). An alternative design approach is covariate-constrained randomization, whereby a randomization scheme is randomly selected from a subset of all possible randomization schemes based on the value of a balancing criterion (Raab and Butcher, 2001, Statistics in Medicine 20: 351–365). Subsequently, a clustered permutation test can be used in the analysis, which provides increased power under constrained randomization compared with simple randomization (Li et al., 2016, Statistics in Medicine 35: 1565–1579). In this article, we describe covariate-constrained randomization and the permutation test for the design and analysis of CRTs and provide an example to demonstrate the use of our new commands cvcrand and cptest to implement constrained randomization and the permutation test.