Joining the Dots – Linking disconnected networks of evidence using dose-response Model-Based Network Meta-Analysis

Purpose: Network meta-analysis (NMA) synthesises direct and indirect evidence on multiple treatments to estimate their relative effectiveness, and it is often used as a source of clinical evidence with which to make cost-effectiveness decisions in Health Technology Appraisals (HTA). However, comparisons between disconnected treatments are not possible without making strong assumptions. When studies including multiple doses of the same drug are available, model-based NMA (MBNMA) presents a novel solution to this problem by modelling a functional dose-response relationship within a NMA framework. Here we illustrate several scenarios in which dose-response MBNMA can connect and strengthen evidence networks and evaluate the reliability of this analysis in illustrative datasets.
Methods: We created 18 illustrative disconnected datasets by removing studies or treatments from a connected network of triptans for migraine relief. We fitted MBNMA models with Emax or Exponential dose-response relationships to each dataset and compared common and random treatment effect models. For connected networks, we compared MBNMA estimates with NMA estimates. For disconnected networks, we compared MBNMA estimates with NMA estimates from an “augmented” network connected by adding studies or treatments back into the dataset.
Results: In connected networks relative effect estimates from MBNMA were more precise than those from NMA models (ratio of posterior standard deviations NMA vs MBNMA: median=1.13; range=1.04-1.68). In disconnected networks MBNMA provided estimates for all treatments where NMA could not and were in agreement with NMA estimates from augmented networks for 15/18 datasets (100% MBNMA posterior densities within 95% credible intervals of NMA estimates). In the remaining 3/18 datasets a more complex dose-response relationship was required than could be fitted with the available disconnected evidence, leading to estimates that were similar but not fully in agreement between NMA and MBNMA models (19%, 40% and 66% MBNMA posterior densities within 95% credible intervals of NMA estimates).
Conclusions: Where information on multiple doses is available, MBNMA can connect disconnected networks and increase precision, whilst making less strong assumptions than alternative approaches. MBNMA relies on correct specification of the dose-response relationship which requires sufficient data at different doses to allow reliable estimation. In HTAs evidence is often only included at licensed doses. We therefore recommend that systematic reviews for HTA search for and include evidence (including phase-II trials) on multiple doses of agents where available.