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

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. Individual patient data (IPD) meta-regression can relax this assumption, but in many cases IPD are only available in 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 model over AgD covariate distributions to incorporate data from IPD and AgD studies and avoid aggregation bias. However, ML-NMR requires the aggregate-level likelihood to have 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.

We extend ML-NMR to handle individual-level likelihoods of 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.

We show how the individual-level likelihood function conditional on the covariates is integrated over the covariate distributions in each AgD study to obtain the respective marginal likelihood contributions. Quasi-Monte Carlo numerical integration is used, making application general.

Joint synthesis of ordered categorical outcomes lead to increased precision compared to separate models. ML-NMR achieved better fit than a random effects NMA, 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.

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.