Modelling time-course relationships with multiple treatments: Model-based network meta-analysis for continuous summary outcomes

Background: Model-based meta-analysis (MBMA) is increasingly used to inform drug-development decisions by synthesising results from multiple studies to estimate treatment, dose-response, and time-course characteristics. Network meta-analysis (NMA) is used in Health Technology Appraisals for simultaneously comparing effects of multiple treatments, to inform reimbursement decisions. Recently, a framework for dose-response model-based network meta-analysis (MBNMA) has been proposed that combines, often nonlinear, MBMA modelling with the statistically robust properties of NMA. Here, we aim to extend this framework to time-course models. Methods: We propose a Bayesian time-course MBNMA modelling framework for continuous summary outcomes that allows for nonlinear modelling of multiparameter time-course functions, accounts for residual correlation between observations, preserves randomisation by modelling relative effects, and allows for testing of inconsistency between direct and indirect evidence on the time-course parameters. We demonstrate our modelling framework using an illustrative dataset of 23 trials investigating treatments for pain in osteoarthritis. Results: Of the time-course functions that we explored, the E-max model gave the best fit to the data and has biological plausibility. Some simplifying assumptions were needed to identify the ET50, due to few observations at early follow-up times. Treatment estimates were robust to the inclusion of correlations in the likelihood. Conclusions: Time-course MBNMA provides a statistically robust framework for synthesising evidence on multiple treatments at multiple time points. The use of placebo-controlled studies in drug-development means there is limited potential for inconsistency. The methods can inform drug-development decisions and provide the rigour needed in the reimbursement decision-making process.