Automated methods to test connectedness and quantify indirectness of evidence in network meta-analysis

Network meta-analysis compares multiple treatments from studies that form a connected network of evidence. However, for complex networks, it is not easy to see if the network is connected. We use simple techniques from graph theory to test the connectedness of evidence networks in network meta-analysis. The method is to build the adjacency matrix for a network, with rows and columns corresponding to the treatments in the network and entries being one or zero depending on whether the treatments have been compared or not, and with zeros along the diagonal. Manipulation of this matrix gives the indirect connection matrix. The entries of this matrix determine whether two treatments can be compared, directly or indirectly. We also describe the distance matrix, which gives the minimum number of steps in the network required to compare a pair of treatments. This is a useful assessment of an indirect comparison as each additional step requires further assumptions of homogeneity in, for example, design and target populations of included trials. If there are no loops in the network, the distance is a measure of the degree of assumptions needed; it is approximately this with loops. We illustrate our methods using several constructed examples and giving R code for computation. We have also implemented the techniques in the Stata package "network." The methods provide a fast way to ensure comparisons are only made between connected treatments and to assess the degree of indirectness of a comparison.