Standard meta-analysis so called  pairwise meta-analysis pools data from several trials which compare only 2 treatments A versus B in an attempt to increase the sample size and highlight potential differences not detected by relatively small individual studies. 

Network pools data from trials comparing different treatment (A vs B; B vs C) in an attempt to find the best treatments when more than 2 treatments have been investigated by individual studies. 

As explained by Benedetto above, Network Meta-analysis is useful for analysing treatment effects when there are more than two possible interventions, with trials comparing different combinations of these (a "network" of trials).  It uses both direct evidence (direct comparisons from published trials) and indirect comparisons (that can be inferred by the results of other comparisons).

Take, for example, three treatments for a condition, A, B and C.  We might have published trials comparing A and B, and trials comparing B and C.  Standard meta-analysis will be able to give us a summary effect for the comparison between A and B and that between B and C. If there are no trials comparing A and C we cannot infer any estimate of the relationship between these two treatments using standard meta-analysis.

But what if A is superior to B, and B is superior to C in standard meta-analysis?  It would seem logical that A is better than C, even though we have no direct evidence comparing the two.  This is what we mean by "indirect" evidence - estimates of treatment effects derived from other routes around the network.

Network meta-analysis uses bayesian modelling to incorporate direct trial evidence and indirect evidence to provide a more precise estimate of the treatment effects.  It is also possible to rank different treatments as to whether they are most likely to be the best treatment, second best treatment etc.

A bayesian approach is not the only method to perform a network metaanalisis. Other frequentist approaches are possible (Lumley T. Network meta-analysis for indirect treatment comparisons. Stat Med. 2002;21(16):2313–24) And there are other ways to carry out indirect comparisons (Bucher HC, Guyatt GH, Griffith LE, Walter SD. The results of direct and indirect treatment comparisons in meta-analysis of randomized controlled trials. J Clin Epidemiol 1997;50:683-91).

However, as a recent research from AHRQ concludes: "Bayesian MTC methods allow investigators to calculate results for many more comparisons of interest for some network patterns, including ladders and complex networks, than frequentist meta-regression or the Bucher method, in the manner that they are typically applied." (Jonas DE, Wilkins TM, Bangdiwala S, et al. Findings of Bayesian Mixed Treatment Comparison Meta-Analyses: Comparison and Exploration Using Real-World Trial Data and Simulation [Internet]. Rockville (MD): Agency for Healthcare Research and Quality (US); 2013 Feb. Available from http://www.ncbi.nlm.nih.gov/books/NBK126109/)

Sorry, but there is a remaining part of the question not answered yet. I do not know what is the role of a network meta analysis (NM) in a systematic review of the literature because I do not know the evidence level corresponding with a NM. I have no clear ideas about NM is "the uppermost level in the evidence hierarchy for decision making, in medicine as well as in other scholarly fields".

Antonio:  to my mind, network meta-analysis is an equivalent evidence level to standard meta-analysis, but uses data in a different way to allow stronger conclusions (if there is consistency) by using both direct and indirect evidence.

Simon, I am very happy to talk to you about this issue. Ciberworld is funny: two days ago I was teaching to a young medical doctors group on searching and retrieving information from referential databases. We use a Problem-Based Learning system and the matter of session was related with a real report that my (former) agency is carrying out: organ preserving systems vs. static cold conservation. Your SRL was (obviously) retrieved and it is currently used by the researcher. Thanks.

You must be right about evidence level of NM, but I am yet on doubt (metaanalysis is not my field). There is several scales used to measuring quality of evidence. All those scales (SIGN, CADTH, Center for EBM, Jadad...) put the metaanalysis (MA) in the first level of evidence, but they are making reference to standard MA, not NM. My concerns about NM are of a epistemological order. Both, MA and MN, are mathematical constructions, but MA is based on comparisons performed in real life, while NM replaces a comparison not yet performed. I trust in mathematics but I have more confidence in the reality. The bases of MA and NM are not the same. The assumptions on control and experimental groups are not the same.

However, Biology or Medicine are not football: Chelsea wins Southampton, Southampton wins Manchester City, Chelsea will win Manchester City?... perhaps (I beg your perdon, I know nothing about football). On the contrary, the physiology and pharmacokynetic of standard human being is more predectible and results from a NM maybe was a faithful reflection of the reality but... is it the reality (called "well conduced RCT")? If a RCT is performed (in the future) on a matter already issued by a NM, even if result from RCT goes in the same direction but is quantitatively different, wich of the two studies will be more reliable? wich of them will be allocated in the top of the table if both differ qualitatively and quantitatively? Clearly, this is a truly scientific (fiction) exercise.

Antonio,  your points are good ones, and I understand your concerns that you are drawing conclusions on (partly) hypothetical comparisons that have not been performed in the real world.  Your football analogy is a good one - it boils down to consistency between direct and indirect evidence.  If A is better than B, and B better than C, then it would be logical to conclude that A is better than C.  But what if you have a trial showing that C is better than A?

There are some safety checks that should be done in network meta-analysis to ensure consistency between direct and indirect evidence (see http://onlinelibrary.wiley.com/doi/10.1002/jrsm.1044/abstract for a good overview).  The more evidence you have, the more sure you can be of your results.  So If you have 3 trials comparing A and B, 4 comparing B and C, but none comparing A and C, then your comparison of A and C will be entirely governed by indirect evidence and it is impossible to check for inconsistency.  If you have even just one trial comparing A and C, your conclusions become much more sound.

In short - both standard meta-analysis and network meta-analysis can be done badly with too little evidence: both will be inferior evidence to a large, well conduced RCT!

Thank you very much, Simon.

Thank you very much Benedetto, Simon and Antonio. Now most of my doubts got cleared on Network and Pair-wise meta-analysis as well as their role in Systematic review.

Simon Robert Knight, thank you for providing the LINK of the article "Consistency and inconsistency in network meta-analysis: concepts and models for multi-arm studies".