  In a network meta-analysis, some of the collected studies may deviate
markedly from the others, for example having very unusual effect sizes. These
deviating studies can be regarded as outlying with respect to the rest of the
network and can be influential on the pooled results. Thus, it could be
inappropriate to synthesize those studies without further investigation. In
this paper, we propose two Bayesian methods to detect outliers in a network
meta-analysis via: (a) a mean-shifted outlier model and (b), posterior
predictive p-values constructed from ad-hoc discrepancy measures. The former
method uses Bayes factors to formally test each study against outliers while
the latter provides a score of outlyingness for each study in the network,
which allows to numerically quantify the uncertainty associated with being
outlier. Furthermore, we present a simple method based on informative priors as
part of the network meta-analysis model to down-weight the detected outliers.
We conduct extensive simulations to evaluate the effectiveness of the proposed
methodology while comparing it to some alternative, available outlier
diagnostic tools. Two real networks of interventions are then used to
demonstrate our methods in practice.
