  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.
