I present methods for assessing the relative effectiveness of two treatments when they have not been compared directly in a randomized trial but have each been compared to other treatments. These network meta-analysis techniques allow estimation of both heterogeneity in the effect of any given treatment and inconsistency ('incoherence') in the evidence from different pairs of treatments. A simple estimation procedure using linear mixed models is given and used in a meta-analysis of treatments for acute myocardial infarction.
Thomas Lumley (2002) studied this question.