Background: Network meta-analysis for multiple treatment comparisons has been a major development in evidence synthesis methodology. However, the validity of a network meta-analysis can be threatened by inconsistency in evidence of the studies in the network. One particular issue of inconsistency is how to evaluate directly the inconsistency between direct and indirect evidence with regard to the effect difference between two treatments. A Bayesian node-splitting model was first proposed and a similar Frequentist side-splitting model has been put forward recently. Yet, it was noted that different parameterizations of side-splitting or node-splitting do not yield the same results when multi-arm trials are involved in the evaluation.

Methods & Results: In this article, we showed that the side-splitting model can be viewed as a special case of design-by-treatment interaction model, and different parameterizations correspond to different design-by-treatment interactions.
We showed how to evaluate the side-splitting model using the arm-based generalized linear mixed model, which is flexible in modeling different types of outcome variables, and an example dataset was used to compare results from the arm-based models to those from the contrast-based models. The three parameterizations of side-splitting make slightly different assumptions: the symmetrical method assumes that both treatments in a treatment contrast contribute to inconsistency between direct and indirect evidence, while the other two parameterizations assume that only one of the two treatments contributes to this inconsistency.

Conclusions: With this understanding in mind, meta-analysts can then make a choice about how to implement the side-splitting method for their analysis.