Theory and practice of Bayesian and frequentist frameworks for network meta-analysis

Network meta-analysis (NMA) is an increasingly popular statistical method of synthesising evidence to assess the comparative benefits and harms of multiple treatments in a single analysis. Several automated software packages facilitate conducting NMA using either of two alternative approaches, Bayesian or frequentist frameworks. Researchers must choose a framework for conducting NMA (Bayesian or frequentist) and select appropriate model(s), and those conducting NMA need to understand the assumptions and limitations of different approaches. Bayesian models are more frequently used and can be more flexible but require checking additional assumptions and greater statistical expertise that are often ignored. The present paper describes the important theoretical aspects of Bayesian and frequentist models for NMA and the applications and considerations of contrast-synthesis and arm-synthesis NMAs. In addition, we present evidence from a limited number of simulation and empirical studies that compared different frequentist and Bayesian models and provide an overview of available automated software packages to perform NMA. We will conclude that when analysts choose appropriate models, there are seldom important differences in the results of Bayesian and frequentist approaches and that network meta-analysts should therefore focus on model features rather than the statistical framework.