A Gentle Introduction to Bayesian Network Meta-Analysis Using an Automated R Package

Abstract

Network meta-analysis is an extension of standard meta-analysis. It allows researchers to build a network of evidence to compare multiple interventions that may have not been compared directly in existing publications. With a Bayesian approach, network meta-analysis can be used to obtain a posterior probability distribution of all the relative treatment effects, which allows for the estimation of relative treatment effects to quantify the uncertainty of parameter estimates, and to rank all the treatments in the network. Ranking treatments using both direct and indirect evidence can provide guidance to policy makers and clinicians for making decisions. The purpose of this paper is to introduce fundamental concepts of Bayesian network meta-analysis (BNMA) to researchers in psychology and social sciences. We discuss several essential concepts of BNMA, including the assumptions of homogeneity and consistency, the fixed and random effects models, prior specification, and model fit evaluation strategies, while pointing out some issues and areas where researchers should use caution in the application of BNMA. Additionally, using an automated R package, we provide a step-by-step demonstration on how to conduct and report the findings of BNMA with a real dataset of psychological interventions extracted from PubMed.

Keywords:

• Bayesian Network meta-analysis
• indirect treatment comparison
• BUGSnet
• post-traumatic stress disorder (PTSD)
• Clinician-Administered PTSD Scale (CAPS)

Notes

1 A treatment effect modifier refers to a third variable that can affect or confound the effects of a treatment on an outcome variable, also known as moderator or covariate in the meta-analysis literature.

2 An arm refers to a group of participants that receives a specific treatment in a clinical trial, and multi-arm trials refer to studies that include more than two arms.

3 It should be noted that in the in BUGSnet R package, precision (i.e., inverse of the variance) is used to define the dispersion in the Bayesian analysis.

4 Spiegelhalter et al. (2002) suggested that pD can be conceptualized as leverages, $pD=\sum \mathit{leverages}$ if a normal linear hierarchical model is used. Leverages can assist to identify influential observations; the higher the leverage values, the more influential the data points are on the parameter estimates. Spiegelhalter et al. proposed leverages plot in which pD can be used with deviance residuals for checking influential observations; this will be illustrated in the step-by-step demonstration.

5 Please note that the full names of the treatment can be found in the note of Appendix. The psychotherapy treatments include three kinds of cognitive behavioral therapy (CBT) based treatments, present centered therapy (PCT), mindfulness, psychoeducation, and somatic treatments.