A Bayesian hierarchical model estimating CACE in meta-analysis of randomized clinical trials with noncompliance

Noncompliance to assigned treatment is a common challenge in analysis and interpretation of randomized clinical trials. The complier average causal effect (CACE) approach provides a useful tool for addressing noncompliance, where CACE is defined as the average difference in potential outcomes for the response in the subpopulation of subjects who comply with their assigned treatments. In this article, we present a Bayesian hierarchical model to estimate the CACE in a meta-analysis of randomized clinical trials where compliance may be heterogeneous between studies. Between-study heterogeneity is taken into account with study-specific random effects. The results are illustrated by a re-analysis of a meta-analysis comparing the effect of epidural analgesia in labor versus no or other analgesia in labor on the outcome cesarean section, where noncompliance varied between studies. Finally, we present simulations evaluating the performance of the proposed approach and illustrate the importance of including appropriate random effects and the impact of overand under-fitting.