An evidence-splitting approach to evaluation of direct-indirect evidence inconsistency in network meta-analysis

Network meta-analysis (NMA) compares the efficacy and harm between several treatments by combining direct and indirect evidence. The validity of NMA requires that all available evidence form a coherent network. Failure to meet such requirement is known as inconsistency. The most popular approach to inconsistency detection is to compare the direct and indirect evidence for each treatment contrast. Although several models have been proposed to evaluate direct-indirect evidence inconsistency, there is no comprehensive study on the implications of how these models separate direct from indirect evidence. The main objective of this study is to show that evidence is not properly split into direct and indirect evidence in current inconsistency models, and to propose a novel approach to inconsistency evaluation based on the principle of independence between direct and indirect evidence. We further demonstrated that current models for direct-indirect evidence inconsistency can potentially lead to misleading conclusions in inconsistency detection and NMA quality appraisal, while our proposed evidence-splitting model satisfies the principle of independence when splitting the direct from indirect evidence in multi-arm trials. Moreover, we showed that all these direct-indirect evidence inconsistency models differ in how the weight of the inconsistency parameter is split between the treatments of interest, yet only the evidence-splitting model assigns satisfying weights. Finally, we demonstrated how the evidence-splitting model can be implemented within the structural equation modeling framework. The evidence-splitting model may be a valuable tool to assess the inconsistency within NMA and evaluate the quality of its evidence.