A Bayesian Framework for Latent Compliance Modeling in Cluster Randomized Trials with One-Sided Noncompliance

In pragmatic cluster randomized controlled trials (PCRCTs), healthcare providers are randomized while both providers and patients may deviate from the assigned intervention. In many PCRCTs, cluster-level implementation is measured using multiple continuous metrics, while individual compliance is recorded as a binary indicator. Standard complier average causal effect (CACE) estimands focus on individual-level compliance and do not account for heterogeneity in implementation across clusters. When intervention uptake is shaped by both provider- and patient-level processes, it is of scientific interest to characterize how effects vary across these sources of compliance. We propose a Bayesian framework for PCRCTs with one-sided binary noncompliance at the individual level and one-sided partial compliance at the cluster level. The method uses a latent mixture model to summarize heterogeneity in cluster-level implementation based on baseline characteristics and observed implementation measures, and links these latent implementation types to individual compliance and outcomes through a joint model. Because compliance is only observed in treated clusters, the model imputes unobserved compliance behavior for clusters and individuals assigned to control. The framework enables estimation of finite- and super-population intent-to-treat (ITT) and CACE estimands, both marginally and within latent implementation types. We apply the method to the METRIcAL trial, a pragmatic cluster randomized study evaluating a personalized music intervention for nursing home residents with dementia. The analysis illustrates how accounting for implementation heterogeneity and individual compliance can provide insights beyond standard ITT analyses.}{Causal inference; Principal stratification; Complier average causal effect; Cluster randomized trials; Noncompliance; Bayesian methods; Latent variable models; Interference.