  Network meta-analysis has been gaining prominence as an evidence synthesis
method that enables the comprehensive synthesis and simultaneous comparison of
multiple treatments. In many network meta-analyses, some of the constituent
studies may have markedly different characteristics from the others, and may be
influential enough to change the overall results. The inclusion of these
"outlying" studies might lead to biases, yielding misleading results. In this
article, we propose effective methods for detecting outlying and influential
studies in a frequentist framework. In particular, we propose suitable
influence measures for network meta-analysis models that involve missing
outcomes and adjust the degree of freedoms appropriately. We propose three
influential measures by a leave-one-trial-out cross-validation scheme: (1)
comparison-specific studentized residual, (2) relative change measure for
covariance matrix of the comparative effectiveness parameters, (3) relative
change measure for heterogeneity covariance matrix. We also propose (4) a
model-based approach using a likelihood ratio statistic by a mean-shifted
outlier detection model. We illustrate the effectiveness of the proposed
methods via applications to a network meta-analysis of antihypertensive drugs.
Using the four proposed methods, we could detect three potential influential
trials involving an obvious outlier that was retracted because of data
falsifications. We also demonstrate that the overall results of comparative
efficacy estimates and the ranking of drugs were altered by omitting these
three influential studies.
