A Latent Principal Stratification Method to Address One-Sided Cluster and Individual Noncompliance in Cluster RCTs

In pragmatic cluster randomized controlled trials (PCRCTs), the unit of randomization may be the healthcare provider. In these studies, noncompliance can occur at both the patient and cluster levels. Some studies measure cluster-level implementation using multiple continuous metrics while documenting individual binary compliance. The complier average causal effect estimates the intervention effects among individuals that comply with the assigned intervention. However, it does not account for compliance metrics at the cluster level. When compliance with the intervention is influenced by both providers and individuals, it can be scientifically beneficial to describe the effects of the intervention between all levels of compliance. We propose a Bayesian method for PCRCTs with one-sided binary noncompliance at the individual level and one-sided partial compliance at the cluster level. Our Bayesian model classifies clusters into latent compliance strata based on pretreatment characteristics, partial compliance status, and individual outcomes. Because compliance is only observed in the treatment arm, the method imputes unobserved compliance for control clusters and the individuals within them. This approach estimates finite and super-population estimands within strata defined by both cluster- and individual-level compliance. We apply this method to the METRIcAL trial, a multi-part, pragmatic cluster randomized trial evaluating the effects of a personalized music intervention on agitation in nursing home residents with dementia.