Bayesian one-step IPD network meta-analysis of time-to-event data using Royston-Parmar models

Network meta-analysis (NMA) combines direct and indirect evidence from trials to calculate and rank treatment estimates. While modelling approaches for continuous and binary outcomes are relatively well developed, less work has been done with time-to-event outcomes. Such outcomes are usually analysed using Cox proportional hazard (PH) models. However, in oncology with longer follow-up time, and time-dependent effects of targeted treatments, this may no longer be appropriate. Network meta-analysis conducted in the Bayesian setting has been increasing in popularity. However, fitting the Cox model is computationally intensive, making it unsuitable for many datasets. Royston-Parmar models are a flexible alternative that can accommodate time-dependent effects. Motivated by individual participant data (IPD) from 37 cervical cancer trials (5922 women) comparing surgery, radiotherapy, and chemotherapy, this paper develops an IPD Royston-Parmar Bayesian NMA model for overall survival. We give WinBUGS code for the model. We show how including a treatment-ln(time) interaction can be used to conduct a global test for PH, illustrate how to test for consistency of direct and indirect evidence, and assess within-design heterogeneity. Our approach provides a computationally practical, flexible Bayesian approach to NMA of IPD survival data, which readily extends to include additional complexities, such as non-PH, increasingly found in oncology trials.