A graphical tool for locating inconsistency in network meta-analyses

Background: In network meta-analyses, several treatments can be compared by connecting evidence from clinical trials that have investigated two or more treatments. The resulting trial network allows estimating the relative effects of all pairs of treatments taking indirect evidence into account. For a valid analysis of the network, consistent information from different pathways is assumed. Consistency can be checked by contrasting effect estimates from direct comparisons with the evidence of the remaining network. Unfortunately, one deviating direct comparison may have side effects on the network estimates of others, thus producing hot spots of inconsistency. Methods: We provide a tool, the net heat plot, to render transparent which direct comparisons drive each network estimate and to display hot spots of inconsistency: this permits singling out which of the suspicious direct comparisons are sufficient to explain the presence of inconsistency. We base our methods on fixed-effects models. For disclosure of potential drivers, the plot comprises the contribution of each direct estimate to network estimates resulting from regression diagnostics. In combination, we show heat colors corresponding to the change in agreement between direct and indirect estimate when relaxing the assumption of consistency for one direct comparison. A clustering procedure is applied to the heat matrix in order to find hot spots of inconsistency. Results: The method is shown to work with several examples, which are constructed by perturbing the effect of single study designs, and with two published network meta-analyses. Once the possible sources of inconsistencies are identified, our method also reveals which network estimates they affect. Conclusion: Our proposal is seen to be useful for identifying sources of inconsistencies in the network together with the interrelatedness of effect estimates. It opens the way for a further analysis based on subject matter considerations.