Observational studies differ from randomised trials in the respect that validity problems cannot be prevented in the study design, e.g. by randomisation, concealed allocation, and blinding. Instead, the statistical analysis needs to include considerations regarding validity oriented adjustments. Please describe in more detail how other sorts of bias than publication bias were evaluated in the review. See also Faber T, Ravaud P, Riveros C, Perrodeau C, Dechartres A. Meta-analyses including non-randomized studies of therapeutic interventions: a methodological review. BMC Medical Research Methodology 2016:35.
The meta-analysis is performed using random-effect models. In contrast to fixed-effect models, which are used to estimate common effects, random-effect models are used to estimate average effects, and the variability of the effects represented by their average may have clinical interpretations. Prediction intervals can be used to evaluate if this is the case here, see e.g. Riley RD, Higgins JPT, Deeks JJ. Research Methods & Reporting: Interpretation of random effects meta-analyses. Br Med J 2011;342:d549. I recommend including prediction intervals in the forest plots.
Network meta-analyses are based on underlying assumptions such as of transitivity, i.e. that there are no systematic differences between the comparisons other than the treatments being compared (see Salanti G. Indirect and mixed-treatment comparison, network, or multiple-treatments meta-analysis: many names, many benefits, many concerns for the next generation evidence synthesis tool. Res Synth Methods 2012;3:80–97). Are these assumptions fulfilled and the calculated effect estimates valid?