  The reliability of the results of network meta-analysis (NMA) lies in the
plausibility of key assumption of transitivity. This assumption implies that
the effect modifiers' distribution is similar across treatment comparisons.
Transitivity is statistically manifested through the consistency assumption
which suggests that direct and indirect evidence are in agreement. Several
methods have been suggested to evaluate consistency. A popular approach
suggests adding inconsistency factors to the NMA model. We follow a different
direction by describing each inconsistency factor with a candidate covariate
whose choice relies on variable selection techniques. Our proposed method,
Stochastic Search Inconsistency Factor Selection (SSIFS), evaluates the
consistency assumption both locally and globally, by applying the stochastic
search variable selection method to determine whether the inconsistency factors
should be included in the model. The posterior inclusion probability of each
inconsistency factor quantifies how likely is a specific comparison to be
inconsistent. We use posterior model odds or the median probability model to
decide on the importance of inconsistency factors. Differences between direct
and indirect evidence can be incorporated into the inconsistency detection
process. A key point of our proposed approach is the construction of a
reasonable "informative" prior concerning network consistency. The prior is
based on the elicitation of information derived historical data from 201
published network meta-analyses. The performance of our proposed method is
evaluated in two published network meta-analyses. The proposed methodology is
publicly available in an R package called ssifs, developed and maintained by
the authors of this work.
