Bayesian model-based outlier detection in network meta-analysis

In 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 synthesise 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, allowing 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 outlier detection tools. Two case studies are then used to demonstrate our methods in practice.