Multilevel network meta-regression for general likelihoods: synthesis of individual and aggregate data with applications to survival analysis

Network meta-analysis combines aggregate data (AgD) from multiple randomized controlled trials, assuming that any effect modifiers are balanced across populations. Individual participant data (IPD) meta-regression is the ‘gold standard’ method to relax this assumption, however IPD are frequently only available in a subset of studies. Multilevel network meta-regression (ML-NMR) extends IPD meta-regression to incorporate AgD studies whilst avoiding aggregation bias. However, implementation of this method so far has required the aggregate-level likelihood to have a known closed form, which has prevented application to time-to-event outcomes. We extend ML-NMR to individual-level likelihoods of any form, by integrating the individual-level likelihood function over the AgD covariate distributions to obtain the respective marginal likelihood contributions. We illustrate with two examples of time-to-event outcomes: modelling progression-free survival in newly diagnosed multiple myeloma using flexible baseline hazards with cubic M-splines, and a simulated comparison showing the performance of ML-NMR with little loss of precision from a full IPD analysis. Extending ML-NMR to general likelihoods, including for survival outcomes, greatly increases the applicability of the method. R and Stan code is provided, and the methods are implemented in the multinma R package.