Influence analyses of "designs" for evaluating inconsistency in network meta-analysis

Network meta-analysis is an evidence synthesis method for comparative effectiveness analyses of multiple available treatments. To justify evidence synthesis, consistency is a relevant assumption; however, existing methods founded on statistical testing possibly have substantial limitations of statistical powers or several drawbacks in treating multi-arm studies. Besides, inconsistency is theoretically explained as design-by-treatment interactions, and the primary purpose of these analyses is prioritizing "designs" for further investigations to explore sources of biases and irregular issues that might influence the overall results. In this article, we propose an alternative framework for inconsistency evaluations using influence diagnostic methods that enable quantitative evaluations of the influences of individual designs to the overall results. We provide four new methods to quantify the influences of individual designs through a "leave-one-design-out" analysis framework. We also propose a simple summary measure, the O-value, for prioritizing designs and interpreting these influential analyses straightforwardly. Furthermore, we propose another testing approach based on the leave-one-design-out analysis framework. By applying the new methods to a network meta-analysis of antihypertensive drugs, we demonstrate the new methods located potential sources of inconsistency accurately. The proposed methods provide new insights into alternatives to existing test-based methods, especially quantifications of influences of individual designs on the overall network meta-analysis results.