Using Generalized Linear Mixed Models to Evaluate Inconsistency within a Network Meta-Analysis

Abstract

Background: Network meta-analysis compares multiple treatments by incorporating direct and indirect evidence into a general statistical framework. One issue with the validity of network meta-analysis is inconsistency between direct and indirect evidence within a loop formed by three treatments. Recently, the inconsistency issue has been explored further and a complex design-by-treatment interaction model proposed.

Objective: The aim of this article was to show how to evaluate the design-by-treatment interaction model using the generalized linear mixed model.

Methods: We proposed an arm-based approach to evaluating the design-by-treatment inconsistency, which is flexible in modeling different types of outcome variables. We used the smoking cessation data to compare results from our arm-based approach with those from the standard contrast-based approach.

Results: Because the contrast-based approach requires transformation of data, our example showed that such a transformation may yield biases in the treatment effect and inconsistency evaluation, when event rates were low in some treatments. We also compared contrast-based and arm-based models in the evaluation of design inconsistency when different heterogeneity variances were estimated, and the arm-based model yielded more accurate results.

Conclusions: Because some statistical software commands can detect the collinearity among variables and automatically remove the redundant ones, we can use this advantage to help with placing the inconsistency parameters. This could be very useful for a network meta-analysis involving many designs and treatments.

Keywords: design-by-treatment interaction; generalized linear mixed models; network meta-analysis; randomized controlled trials.