Meta-analysis of interventions usually relies on randomized controlled trials. However, when the dominant source of information comes from single-arm studies, or when the results from randomized controlled trials lack generalization due to strict inclusion and exclusion criteria, it is vital to synthesize both sources of evidence. One challenge of synthesizing both sources is that single-arm studies are usually less reliable than randomized controlled trials due to selection bias and confounding factors. In this paper, we propose a Bayesian hierarchical framework for the purpose of bias reduction and efficiency gain. Under this framework, three methods are proposed: bivariate generalized linear mixed effects models, hierarchical power prior model and hierarchical commensurate prior model. Design difference and potential biases are considered in all models, within which the hierarchical power prior and hierarchical commensurate prior models further offer to downweight single-arm studies flexibly. The hierarchical commensurate prior model is recommended as the primary method for evidence synthesis because of its accuracy and robustness. We illustrate our methods by applying all models to two motivating datasets and evaluate their performance through simulation studies. We finish with a discussion of the advantages and limitations of our methods, as well as directions for future research in this area.
Keywords: Evidence synthesis; Markov chain Monte Carlo; bias; different types of studies; downweighting; efficiency.