The bipartite structure of treatment-trial networks reveals the flow of information in network meta-analysis

Network meta-analysis (NMA) combines evidence from multiple trials comparing treatments for the same condition. The name derives from a graphical representation of the data where nodes are treatments, and edges represent comparisons between treatments in trials. However, edges in this graph are limited to pairwise comparisons and fail to represent trials that compare more than two treatments. In this paper, we describe NMA as a bipartite graph where trials define a second type of node. Edges then correspond to the arms of trials, connecting each trial node to the treatments it compares. By linking the hat matrix of the NMA model to the bipartite framework, we reveal how evidence flows through the arms of trials. We then define a random walk on the bipartite graph and propose two conjectures relating the movement of this walker to evidence flow. We illustrate our methods on a network of treatments for plaque psoriasis and verify our conjectures in simulations on randomly generated graphs. Moreover, these simulations demonstrate that simulating bipartite graphs overcomes the challenges involved in generating networks with multi-arm trials. The bipartite framework provides new insights into the evidence structure of NMA and the role of individual trials in producing NMA estimates.