Multivariate Network Meta-Analysis of Survival Function Parameters

Background: Network meta-analysis (NMA) of survival data with a multidimensional treatment effect has been introduced as an alternative to NMA based on the proportional hazards assumption. However, these flexible models have some limitations, such as the use of an approximate likelihood based on discrete hazards, rather than a likelihood for individual event times. The aim of this article is to overcome the limitations and present an alternative implementation of these flexible NMA models for time-to-event outcomes with a two-step approach. Methods: First, for each arm of every randomised controlled trial (RCT) connected in the network of evidence, reconstructed patient data are fit to alternative survival distributions, including the exponential, Weibull, Gompertz, log-normal, and log-logistic. Next, for each distribution, its scale and shape parameters are included in a multivariate NMA to obtain time-varying estimates of relative treatment effects between competing interventions. Results: An illustrative analysis is presented for a network of RCTs evaluating multiple interventions for advanced melanoma regarding overall survival. Alternative survival distributions were compared based on model fit criteria. Based on the log-logistic distribution, the difference in shape and scale parameters for each treatment versus dacarbazine (DTIC) was identified and the corresponding log hazard and survival curves were presented. Conclusions: The presented two-step NMA approach provides an evidence synthesis framework for time-to-event outcomes grounded in standard practice of parametric survival analysis. The method allows for a more transparent and efficient model selection process.