Extending DerSimonian and Laird's methodology to perform network meta-analyses with random inconsistency effects.

Network meta-analysis is becoming more popular as a way to compare multiple treatments simultaneously. Here, we develop a new estimation method for fitting models for network meta-analysis with random inconsistency effects. This method is an extension of the procedure originally proposed by DerSimonian and Laird. Our methodology allows for inconsistency within the network. The proposed procedure is semi-parametric, non-iterative, fast and highly accessible to applied researchers. The methodology is found to perform satisfactorily in a simulation study provided that the sample size is large enough and the extent of the inconsistency is not very severe. We apply our approach to two real examples.