A multilevel approach to network meta-analysis within a frequentist framework

Meta-analysis is a powerful tool to summarize knowledge. Pairwise or network meta-analysis may be carried out with multivariate models that account for the dependence between treatment estimates and quantify the correlation across studies. From a different perspective, meta-analysis may be viewed as a special case of multilevel analysis having a hierarchical data structure. Hence, we introduce an alternative frequentist approach, called multilevel network meta-analysis, which also allows to account for publication bias and the presence of inconsistency. We propose our approach for a three-level data structure set-up: arms within studies at the first level, studies within study designs at the second level and design configuration at the third level. This strategy differs from the traditional frequentist modeling because it works directly on an arm-based data structure. An advantage of using multilevel analysis is its flexibility, since it naturally allows to add further levels to the model and to accommodate for multiple outcome variables. Moreover, multilevel modeling may be carried out with widely available statistical programs. Finally, we compare the results from our approach with those from a Bayesian network meta-analysis on a binary endpoint which examines the effect on mortality of some anesthetics at the longest follow-up available. In addition, we compare results from the Bayesian and multilevel network meta-analysis approaches on a publicly available "Thrombolytic drugs" database. We also provide the reader with a blueprint of SAS codes for fitting the proposed models, although our approach does not rely on any specific software.