Network meta-analysis of individual and aggregate level data.

Network meta-analysis is often performed with aggregate-level data (AgD). A challenge in using AgD is that the association between a patient-level covariate and treatment effects at the study level may not reflect the individual-level effect modification. In this paper, non-linear network meta-analysis models for combining individual patient data (IPD) and AgD are presented to reduce bias and uncertainty of direct and indirect treatment effects in the presence of heterogeneity. The first method uses the same model form for IPD and AgD. With the second method, the model for AgD is obtained by integrating an underlying IPD model over the joint within-study distribution of covariates, in line with the method by Jackson et al. for ecological inferences. With simulated examples, the models are illustrated. Having IPD for a subset of studies improves estimation of treatment effects in the presence of patient-level heterogeneity. Of the two proposed non-linear models for combining IPD and AgD, the second seems less affected by bias in situations with large treatment-by-patient-level-covariate interactions, probably at the cost of greater uncertainty. Additional studies are needed to better understand when one model is favorable over the other. For network meta-analysis, it is recommended to use IPD when available.