Bayesian Causal Inferencee In Meta-Analysis

Abstract

While the randomized clinical trial (RCT) is the gold standard for investigating the effect of a medical intervention, noncompliance to assigned treatments can threaten a trial's validity. Noncompliance, if not appropriately controlled, can introduce substantial bias into the estimate of treatment effect. The complier average causal effect (CACE) approach provides a useful tool for addressing noncompliance, where CACE measures the effect of an intervention in the latent subgroup of the study population that complies with its assigned treatment (the compliers). Meta-analysis of RCTs has become a widely-used statistical technique to combine and contrast results from multiple independent studies. However, no existing methods can effectively deal with heterogeneous noncompliance in meta-analysis of RCTs. For example, the commonly used meta-analysis regression methods investigate the impact of study-level variables (e.g., mean age of the study population) on the study-specific treatment effect size by assuming the study-level covariates to be fixed. However, noncompliance rates generally differ between treatment groups within a study and are commonly considered as random rather than fixed post-randomization variables. In addition, noncompliance may dynamically interact with the primary outcome and thus affect the response to treatment. Thus, meta-regression methods are not suitable to controlling for noncompliance. This thesis focuses on developing Bayesian methods to estimate CACE in meta-analysis of RCTs with binary or ordinal outcomes. Bayesian hierarchical random effects models are developed to appropriately account for the inherent heterogeneity in treatment effect and noncompliance between studies and treatment groups. We first present a Bayesian hierarchical model to estimate the CACE where heterogeneous compliance rates are available for each study. Second, we extend our approach to deal with incomplete noncompliance when some RCTs do not report noncompliance data. 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 varies substantially between studies. Simulations are performed to evaluate the performance of the proposed approach and to illustrate the importance of including appropriate random effects by showing the impact of over- and under-fitting. Furthermore, we develop an R package, BayesCACE, to provide user-friendly functions to implement CACE analysis for binary outcomes based on the proposed Bayesian hierarchical models. This package includes flexible functions for analyzing data from a single RCT and from a meta-analysis of multiple RCTs with either complete or incomplete noncompliance data. The package also provides various functions for generating forest, trace, posterior density, and auto-correlation plots, and to review noncompliance rates, visually assess the model, and obtain study-specific and overall CACEs.