Network meta-analysis models to account for variability in treatment definitions: application to dose effects

For a network meta-analysis, an interlinked network of nodes representing competing treatments is needed. It is often challenging to define the nodes as these typically refer to similar but rarely identical interventions. The objectives of this paper are as follows: (i) to present a series of network meta-analysis models that account for variation in the definition of the nodes and (ii) to exemplify the models where variation in the treatment definitions relates to the dose. Starting from the model that assumes each node has a 'fixed' definition, we gradually introduce terms to explain variability by assuming that each node has several subnodes that relate to different doses. The effects of subnodes are considered monotonic, linked with a 'random walk', random but exchangeable, or have a linear pattern around the treatment mean effect. Each model can be combined with different assumptions for the consistency of effects and might impact on the ranking of the treatments. Goodness of fit, heterogeneity and inconsistency were assessed. The models are illustrated in a star network for the effectiveness of fluoride toothpaste and in a full network comparing agents for multiple sclerosis. The fit and parsimony measures indicate that in the fluoride network the impact of the dose subnodes is important whereas in the multiple sclerosis network the model without subnodes is the most appropriate. The proposed approach can be a useful exploratory tool to explain sources of heterogeneity and inconsistency when there is doubt whether similar interventions should be grouped under the same node.