Is there a method/package that combines multivariate and network meta-analysis?

Question

If you want to perform a meta-analysis on the general strength of the population and where each study can offer multiple outcomes (for example, measuring strength through deadlift capability and/or the number of push-ups someone can do), you normally use a multivariate meta-analysis (for example the rma.mv function in the R package metafor).

If you, on the other hand, want to perform a meta-analysis on how different drugs affect strength and where each study can offer results from one or many different type of treatments (for example, drug A, drug B, and/or drug C), you normally use a network meta-analysis (for example, the netmeta function in the R package netmeta).

However, what do you do if you want to performa a meta-analysis on how different drugs affect strength and where each study can offer results from one or many different type of treatments as well as well as multiple outcomes (for example, effectiveness of drug A, drug B, and/or drug C, measured through deadlift capability and/or the number of push-ups someone can do)? I have searched high and low for a statistical method and/or package that combines the two approaches described above into one, but so far, I've come up short.

My question is meant to be as general as possible with the concrete examples only placed there for clarity. So, in the example above, you could probably perform two network meta-analyses, one for each type of outcome. However, this might not always be possible to do, for example if the different type of outcomes are hard to cluster into comparable groups (and where you only assume that they, with enough study, will average out to something comparable, just as you do in a multivariate meta-analysis).

Answer 1

You can conduct network meta-analyses also with metafor. See help(rma.mv) and see these examples:

• https://wviechtb.github.io/metadat/reference/dat.hasselblad1998.html
• https://wviechtb.github.io/metadat/reference/dat.senn2013.html
• https://wviechtb.github.io/metadat/reference/dat.pagliaro1992.html
• https://wviechtb.github.io/metadat/reference/dat.lopez2019.html

None of these examples include the analysis of two or more outcomes, but since rma.mv() provides a very general modeling framework, one could combine the ideas of a multivariate and network meta-analysis in a single model.

Relevant articles are:

Achana, F. A., Cooper, N. J., Bujkiewicz, S., Hubbard, S. J., Kendrick, D., Jones, D. R., & Sutton, A. J. (2014). Network meta-analysis of multiple outcome measures accounting for borrowing of information across outcomes. BMC Medical Research Methodology, 14(92). https://doi.org/10.1186/1471-2288-14-92

Efthimiou, O., Mavridis, D., Cipriani, A., Leucht, S., Bagos, P., & Salanti, G. (2014). An approach for modelling multiple correlated outcomes in a network of interventions using odds ratios. Statistics in Medicine, 33(13), 2275-2287. https://doi.org/10.1002/sim.6117

Riley, R. D., Jackson, D., Salanti, G., Burke, D. L., Price, M., Kirkham, J., & White, I. R. (2017). Multivariate and network meta-analysis of multiple outcomes and multiple treatments: Rationale, concepts, and examples. British Medical Journal, 358. https://doi.org/10.1136/bmj.j3932

The methodology presented there makes use of Bayesian methods, but one could also specify analogous models using rma.mv().