Switching Cluster Membership in Cluster Randomized Control Trials

Randomized control trials (RCTs) often use clustered designs, where intact clusters (such as classroom, schools, or treatment centers) are randomly assigned to treatment and control conditions. Hierarchical linear models (HLMs) are used almost universally to estimate the effects in such experiments. While study designs that utilize intact clusters have many potential advantages, there is little guidance in the literature on how to respond when cluster switching induces noncompliance with the randomization protocol. In the presence of noncompliance the intent-to-treat (ITT) effect becomes the estimand of interest. When fitting the HLM, these individuals who switch clusters can be assigned to either their as-assigned cluster (the cluster they belonged to at the time of randomization) or their as-treated cluster (the cluster they belonged to at the time the outcome was collected). We show analytically and via simulation, that using the as-treated cluster in HLM will bias the estimate of the ITT effect and using the as-assigned cluster will bias the standard error estimates when heterogeneity among clusters is because of heterogeneity in treatment effects. We show that using linear regression with two-way cluster adjusted standard errors can yield unbiased ITT estimates and consistent standard errors regardless of the source of the random effects. We recommend this method replace HLM as the method of choice for testing intervention effects with cluster-randomized trials with noncompliance and cluster switching.