Challenges of modelling approaches for network meta-analysis of time-to-event outcomes in the presence of non-proportional hazards to aid decision making: Application to a melanoma network

Background Synthesis of clinical effectiveness from multiple trials is a well-established component of decision-making. Time-to-event outcomes are often synthesised using the Cox proportional hazards model assuming a constant hazard ratio over time. However, with an increasing proportion of trials reporting treatment effects where hazard ratios vary over time and with differing lengths of follow-up across trials, alternative synthesis methods are needed. Objectives To compare and contrast five modelling approaches for synthesis of time-to-event outcomes and provide guidance on key considerations for choosing between the modelling approaches. Methods The Cox proportional hazards model and five other methods of estimating treatment effects from time-to-event outcomes, which relax the proportional hazards assumption, were applied to a network of melanoma trials reporting overall survival: restricted mean survival time, generalised gamma, piecewise exponential, fractional polynomial and Royston-Parmar models. Results All models fitted the melanoma network acceptably well. However, there were important differences in extrapolations of the survival curve and interpretability of the modelling constraints demonstrating the potential for different conclusions from different modelling approaches. Conclusion The restricted mean survival time, generalised gamma, piecewise exponential, fractional polynomial and Royston-Parmar models can accommodate non-proportional hazards and differing lengths of trial follow-up within a network meta-analysis of time-to-event outcomes. We recommend that model choice is informed using available and relevant prior knowledge, model transparency, graphically comparing survival curves alongside observed data to aid consideration of the reliability of the survival estimates, and consideration of how the treatment effect estimates can be incorporated within a decision model.