Visualizing the flow of evidence in network meta-analysis and characterizing mixed treatment comparisons

Network meta-analysis techniques allow for pooling evidence from different studies with only partially overlapping designs for getting a broader basis for decision support. The results are network-based effect estimates that take indirect evidence into account for all pairs of treatments. The results critically depend on homogeneity and consistency assumptions, which are sometimes difficult to investigate. To support such evaluation, we propose a display of the flow of evidence and introduce new measures that characterize the structure of a mixed treatment comparison. Specifically, a linear fixed effects model for network meta-analysis is considered, where the network estimates for two treatments are linear combinations of direct effect estimates comparing these or other treatments. The linear coefficients can be seen as the generalization of weights known from classical meta-analysis. We summarize properties of these coefficients and display them as a weighted directed acyclic graph, representing the flow of evidence. Furthermore, measures are introduced that quantify the direct evidence proportion, the mean path length, and the minimal parallelism of mixed treatment comparisons. The graphical display and the measures are illustrated for two published network meta-analyses. In these applications, the proposed methods are seen to render transparent the process of data pooling in mixed treatment comparisons. They can be expected to be more generally useful for guiding and facilitating the validity assessment in network meta-analysis.