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 Using the four proposed methods, we could detect three potential influential trials involving an obvious outlier that was retracted because of data falsifications.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. K E Y W O R D S contrast-based model, influence diagnostics, multivariate meta-analysis, network meta-analysis, outlier detection 1 | INTRODUCTION Network meta-analysis has been gaining prominence as an evidence synthesis method that enables the comprehensive synthesis and simultaneous comparison of multiple treatments. The methodology can synthesize both direct and indirect evidence for all treatment comparisons of interest, and provides estimates of comparative efficacies among treatments, even when no direct comparison evidence exists for some of the included treatments. 1,2 In network meta-analysis, there are often systematic heterogeneities among the synthesized studies, for example, study designs, participant characteristics, regions, sites, treatment administration, interventions, outcome definitions, and so on. Therefore, heterogeneity of the