Graphical exploration of network meta-analysis data: the use of multidimensional scaling

Evidence synthesis is increasingly being used to compare more than two treatments from multiple randomized trials. In a network of randomized comparisons, direct (head-to-head) evidence might be inconsistent with indirect evidence. However, the issue of potential incoherence of the network is not taken into account in statistical models with fixed treatment effects only, which are commonly employed in practice.

We present a graphical method to summarize a network of randomized comparisons and to examine the incoherence of the network, without making any distributional assumptions.

At each treatment-pair level, the inverse variance method is used to pool results from multiple studies. We consider the magnitude of pairwise treatment contrasts as a measure of pairwise dissimilarity. We summarize a network of randomized comparisons as a dissimilarity matrix, and then apply weighted multidimensional scaling to the dissimilarity matrix. The weights are chosen according to the inverse variance method. We show that, with this weighting scheme, 1D multidimensional scaling configuration is closely related to a fixed effect model. Therefore, our interest is to explore a departure from 1D constraint.

Two-dimensional multidimensional scaling configuration is useful to explore the incoherence of the network. Our method is illustrated with two published datasets.

The weighting scheme in our multidimensional scaling setting is chosen to be optimal for independent treatment pairs. Pairwise differences within a multi-arm trial are correlated to one another and intrinsically coherent. Thus our weighting scheme may not apply to data with large numbers of multi-arm trials.

Multidimensional scaling provides a useful tool for investigators to visualize the network of randomized comparisons and to assess incoherence of the network.