There is a possibility to conduct a network meta-regression by adding study variables as moderators. Here is a link to the NICE guidelines with theoretical background and useful examples: http://www.nicedsu.org.uk/TSD3%20Heterogeneity.final%20report.08.05.12.pdf. I hope you can find all information you need there.
I'd also recommend the report noted above, TSD3 from the NICE technical support document series. you'll find code for bayesian applications with code there. an easy way to find published examples is to google search something like "network meta-analysis AND regression" and browse through. here is one of many possible examples out there:
Comparative tolerability and harms of individual statins: a study-level network meta-analysis of 246 955 participants from 135 randomized, controlled trials.