cvcrand and cptest: Efficient design and analysis of cluster randomized trials

Cluster randomized trials (CRTs), where clusters (for example, schools or clinics) are randomized but measurements are taken on individuals, are commonly used to evaluate interventions in public health and social science. Because CRTs typically involve only a few clusters, simple randomization frequently leads to baseline imbalance of cluster characteristics across treatment 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). An alternative approach is constrained randomization, whereby an allocation scheme is randomly selected from a subset of all possible allocation schemes based on the value of a balancing criterion (Raab and Butcher 2001). Subsequently, an adjusted permutation test can be used in the analysis, which provides increased efficiency under constrained randomization compared with simple randomization (Li et al. 2015). We describe constrained randomization and permutation tests for the design and analysis of CRTs and provide examples to demonstrate the use of our newly created Stata package (cvcrand), which uses Mata to efficiently process large allocation matrices—to implement constrained randomization and permutation tests.