Hierarchical network meta-analysis models for synthesis of evidence from randomised and non-randomised studies

BACKGROUND: With the increased interest in the inclusion of non-randomised data in network meta-analyses (NMAs) of randomised controlled trials (RCTs), analysts need to consider the implications of the differences in study designs as such data can be prone to increased bias due to the lack of randomisation and unmeasured confounding. This study aims to explore and extend a number of NMA models that account for the differences in the study designs, assessing their impact on the effect estimates and uncertainty. METHODS: Bayesian random-effects meta-analytic models, including naïve pooling and hierarchical models differentiating between the study designs, were extended to allow for the treatment class effect and accounting for bias, with further extensions allowing for bias terms to vary depending on the treatment class. Models were applied to an illustrative example in type 2 diabetes; using data from a systematic review of RCTs and non-randomised studies of two classes of glucose-lowering medications: sodium-glucose co-transporter 2 inhibitors and glucagon-like peptide-1 receptor agonists. RESULTS: Across all methods, the estimated mean differences in glycated haemoglobin after 24 and 52 weeks remained similar with the inclusion of observational data. The uncertainty around these estimates reduced when conducting naïve pooling, compared to NMA of RCT data alone, and remained similar when applying hierarchical model allowing for class effect. However, the uncertainty around these effect estimates increased when fitting hierarchical models allowing for the differences in study design. The impact on uncertainty varied between treatments when applying the bias adjustment models. Hierarchical models and bias adjustment models all provided a better fit in comparison to the naïve-pooling method. CONCLUSIONS: Hierarchical and bias adjustment NMA models accounting for study design may be more appropriate when conducting a NMA of RCTs and observational studies. The degree of uncertainty around the effectiveness estimates varied depending on the method but use of hierarchical models accounting for the study design resulted in increased uncertainty. Inclusion of non-randomised data may, however, result in inferences that are more generalisable and the models accounting for the differences in the study design allow for more detailed and appropriate modelling of complex data, preventing overly optimistic conclusions. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s12874-023-01925-5.