Evaluating network meta-analysis and inconsistency using arm-parameterized model in structural equation modeling

Network meta-analysis (NMA) uses both direct and indirect evidence to compare the efficacy and harm between several treatments. Structural equation modeling (SEM) is a statistical method that investigates relations among observed and latent variables. Previous studies have shown that the contrast-based Lu-Ades model for NMA can be implemented in the SEM framework. However, the Lu-Ades model uses the difference between treatments as the unit of analysis, thereby introducing correlations between observations. The main objective of this study is to demonstrate how to undertake NMA in SEM using the outcome of treatment arms as the unit of analysis (arm-parameterized model) and to evaluate direct-indirect evidence inconsistency under this framework. We then showed that our models can include trials of within-person designs without the need for complex data manipulation. Moreover, we showed that a novel approach to meta-analysis, the unrestricted weighted least squares, can be readily extended to NMA under our framework. Finally, we demonstrated that the direct-indirect evidence inconsistency can be evaluated by using multiple group analysis in SEM. We then proposed a novel arm-parameterized inconsistency model for inconsistency evaluation. We applied the proposed models to two NMA datasets and showed that our approach yielded results identical to the Lu-Ades model. We also showed that relaxing variance assumptions can reduce the confidence intervals for certain treatment contrasts, thereby yielding greater statistical power. The arm-parameterized inconsistency model unifies current approaches to inconsistency evaluation.