Quantifying indirect evidence in network meta-analysis.

Network meta-analysis enables comprehensive synthesis of evidence concerning multiple treatments and their simultaneous comparisons based on both direct and indirect evidence. A fundamental pre-requisite of network meta-analysis is the consistency of evidence that is obtained from different sources, particularly whether direct and indirect evidence are in accordance with each other or not, and how they may influence the overall estimates. We have developed an efficient method to quantify indirect evidence, as well as a testing procedure to evaluate their inconsistency using Lindsay's composite likelihood method. We also show that this estimator has complete information for the indirect evidence. Using this method, we can assess the degree of consistency between direct and indirect evidence and their contribution rates to the overall estimate. Sensitivity analyses can be also conducted with this method to assess the influences of potentially inconsistent treatment contrasts on the overall results. These methods can provide useful information for overall comparative results that might be biased from specific inconsistent treatment contrasts. We also provide some fundamental requirements for valid inference on these methods concerning consistency restrictions on multi-arm trials. In addition, the efficiency of the developed method is demonstrated based on simulation studies. Applications to a network meta-analysis of 12 new-generation antidepressants are presented.