Multilevel network meta-regression for population adjustment based on individual and aggregate level data

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.
In the simplest scenario, IPD are available for an AB study but only AgD for an AC study. Methods such as Matching Adjusted Indirect Comparison (MAIC) create a population-adjusted indirect comparison between treatments B and C. However, the resulting comparison is only valid in the AC population without additional assumptions, and the methods cannot be extended to larger treatment networks. Meta-regression-based approaches can be used in larger networks. However, these typically fit the same model at both the individual and aggregate level which incurs aggregation bias.
We propose a general method for synthesising evidence from individual and aggregate data in networks of all sizes, Multilevel Network Meta-Regression, extending the standard NMA framework. An individual-level regression model is defined, and aggregate study data are fitted by integrating this model over the covariate distributions of the respective studies. Since integration is often complex or even intractable, we take a flexible numerical approach using Quasi-Monte Carlo integration, allowing for easy implementation regardless of model form or complexity. Correlation structures between covariates are accounted for using copulae.
We illustrate the method using an example and compare the results to those obtained using current methods. Where heterogeneity may be explained by imbalance in effect modifiers between studies we achieve similar fit to a random effects NMA, but uncertainty is substantially reduced, and the model is more interpretable. Crucially for decision making, comparisons may be provided in any target population with a given covariate distribution.