A Bayesian Hierarchical CACE Model Accounting for Incomplete Noncompliance With Application to a Meta-analysis of Epidural Analgesia on Cesarean Section.

Noncompliance with assigned treatments is a common challenge in analyzing and interpreting randomized clinical trials (RCTs). One way to handle noncompliance is to estimate the complier-average causal effect (CACE), the intervention's efficacy in the subpopulation that complies with assigned treatment. In a two-step meta-analysis, one could first estimate CACE for each study, then combine them to estimate the population-averaged CACE. However, when some trials do not report noncompliance data, the two-step meta-analysis can be less efficient and potentially biased by excluding these trials. This paper proposes a flexible Bayesian hierarchical CACE framework to simultaneously account for heterogeneous and incomplete noncompliance data in a meta-analysis of RCTs. The models are motivated by and used for a meta-analysis estimating the CACE of epidural analgesia on cesarean section, in which only 10 of 27 trials reported complete noncompliance data. The new analysis includes all 27 studies and the results present new insights on the causal effect after accounting for noncompliance. Compared to the estimated risk difference of 0.8% (95% CI: -0.3%, 1.9%) given by the two-step intention-to-treat meta-analysis, the estimated CACE is 4.1% (95% CrI: -0.3%, 10.5%). We also report simulation studies to evaluate the performance of the proposed method.