Graphs of study contributions and covariate distributions for network meta-regression

Meta-regression results must be interpreted taking into account the range of covariate values of the contributing studies. Results based on interpolation or extrapolation may be unreliable. In network meta-regression (NMR) models, which include covariates in network meta-analyses, results are estimated using direct and indirect evidence; therefore, it may be unclear which studies and covariate values contribute to which result. We propose graphs to help understand which trials and covariate values contribute to each NMR result and to highlight extrapolation or interpolation.

We introduce methods to calculate the contribution that each trial and covariate value makes to each result and compare them with existing methods. We show how to construct graphs including a network covariate distribution diagram, covariate-contribution plot, heat plot, contribution-NMR plot, and heat-NMR plot. We demonstrate the methods using a dataset with treatments for malaria using the covariate average age and a dataset of topical fluoride interventions for preventing dental caries using the covariate randomisation year.

For the malaria dataset, no contributing trials had an average age between 7-25 years and therefore results were interpolated within this range. For the fluoride dataset, there are no contributing trials randomised between 1954-1959 for most comparisons therefore, within this range, results would be extrapolated.

Even in a fully connected network, an NMR result may be estimated from trials with a narrower covariate range than the range of the whole dataset. Calculating contributions and graphically displaying them aids interpretation of NMR result by highlighting extrapolated or interpolated results.