Keywords: causal effect, meta-analysis, noncompliance, Bayesian hierarchical model, randomized trial, random effects model
Noncompliance to assigned treatments is a common challenge in the analysis and interpretation of randomized clinical trials. The complier average causal effect (CACE) estimation approach provides a useful tool for addressing noncompliance, where CACE is defined as the average difference in potential outcomes for the response in a subpopulation of subjects who comply with their assigned treatments. In this article, we present a Bayesian hierarchical model to estimating the CACE in a meta-analysis where the compliance information may be heterogeneous among studies or centers. Between-study heterogeneity are taken into account with study-specific random effects. The results are illustrated through reanalyzing the multiple risk factor intervention trial (MRFIT), where non-compliance of smoking rates vary across centers, and a meta-analysis comparing epidural analgesia to no/other analgesia in labor on the outcome of cesarean section, where noncompliance vary across studies. Finally, we conduct comprehensive simulations to evaluate the performance of the proposed approach, and illustrate the importance of including appropriate random effects and the impact of over- and under- fitting.