In scientific research, multiple studies on the same intervention occur for many reasons, such as using different study populations or designs. Research synthesis attempts to integrate different data on the same topic for the purpose of making generalizations, and provides us with a formal method to systematically combine all available evidence. In this thesis, we focus on the synthesis of evidence from multiple clinical trials using network meta-analysis, and the more challenging problem of combining information from randomized clinical trials and less rigorous observational studies. Network meta-analysis (NMA) is an extension of standard pairwise meta-analysis to permit combination of results on more than two treatments. This enables both direct and indirect comparisons of treatments, and addresses the comparative effectiveness or safety of the treatments based on all sources of data. Current NMA methods are usually based on a contrast-based (CB) model to estimate the relative treatment effects for each study. While popular and often effective, this model suffers from certain limitations. An alternative is the arm-based (AB) model, which estimates the mean response directly for each treatment. Compared to the CB framework, AB models are more straightforward to interpret, especially when implemented in a missing-data framework, by allowing use of a common baseline treatment across all trials. In a NMA, when direct and indirect evidence differ, the analysis is said to suffer from inconsistency, and the treatment effect estimates may be biased. Inconsistency detection methods using CB models have already been developed, but no corresponding method based on the newer AB models has yet been proposed. Here, we develop a Bayesian AB approach to detecting inconsistency. After detecting inconsistency, formal diagnostic tests should be performed to check whether this violation of assumption results in the change of treatment effects. Therefore, we next explore whether the trial-arm combinations that are sources of inconsistency are influential or outlying observations. To do this, we modify the "constraint case" method to produce diagnostics suitable for generalized linear models in NMA using either AB or CB models, where the outcome is binary. Lastly, we develop methods to combine the data from a randomized clinical trial and a propensity score-matched non-randomized study using commensurate priors. The approach determines the proper degree of borrowing from the non-randomized data by the similarity of the estimated treatment effects in the two studies. Performance of all our methods is evaluated via both example datasets and simulation studies. In summary, this dissertation work enables improved research synthesis in biomedical applications and sheds light on future research directions in the aforementioned areas.