Synthesis of individual and aggregate level data using multilevel network meta-regression: extension to general likelihoods

Context: Standard network meta-analysis (NMA) and indirect comparisons combine aggregate data (AgD) from multiple studies on treatments of interest, assuming that any effect modifiers are balanced across populations. We can relax this assumption if individual patient data (IPD) are available from all studies by fitting an IPD meta-regression. However, in many cases IPD are only available from a subset of studies. Multilevel Network Meta-Regression (ML-NMR) is a recently-proposed method which extends the IPD meta-regression framework by integrating the individual-level likelihood over AgD covariate distributions to properly incorporate data from IPD and AgD studies and avoid aggregation bias. However, as originally proposed ML-NMR is only applicable when the aggregate-level likelihood has a known closed form. Most notably, this precludes the application of ML-NMR to synthesis of time-to-event outcomes, which make up the large majority of population adjustment analyses to date.
Objective(s): We extend the ML-NMR framework to handle individual-level likelihoods of any general form, illustrating with two examples – a real network of plaque psoriasis treatments with ordered categorical outcomes, and a simulated comparison of time-to-event outcomes.
Method(s): We show how the individual-level likelihood function conditional on the covariates is integrated over the covariate distributions in the AgD studies to obtain the respective marginal likelihood contributions. Integration is performed numerically using quasi-Monte Carlo integration, allowing for general application regardless of model form or covariate distributions.
Results: Joint synthesis of ordered categorical outcomes lead to increased precision compared to separate models and avoided computational difficulties due to few events on higher outcomes. ML-NMR achieved similar fit to a random effects Non of effect estimates relevant to the decision target population.MA, but uncertainty was substantially reduced, and the model was more interpretable. For the simulated survival data, ML-NMR agreed closely with the known truth, with little loss of precision from a full IPD analysis.
Conclusions: ML-NMR is a flexible and general method for synthesising evidence from mixtures of individual and aggregate level data in networks of all sizes. Extension to general likelihoods, including for survival outcomes, greatly increases the applicability of the method. Decision making is aided by the production of effect estimates relevant to the decision target population.