boutliers: R package of outlier detection and influence diagnostics for meta-analysis

Meta-analysis is an established methodology for evidence synthesis. In practice, substantial heterogeneity often arises among studies, and random-effects models are widely employed as standard tools. However, in many cases of data synthesis, some studies exhibit markedly different characteristics from others, beyond the degree expected from statistical error, and may become influential outliers that affect the overall conclusions. Although outlier detection and influence diagnostic methods have been discussed in the context of meta-analysis, there has been a lack of user-friendly statistical packages that quantify the statistical uncertainty of diagnostic measures. We developed the R package boutliers, which implements influence diagnostics based on bootstrap methods using simple commands. The package provides three leave-one-out diagnostics: (1) studentized residuals, (2) relative change measures for the variance of the grand mean parameter, and (3) relative change measures for heterogeneity variance. In addition, a model-based approach using a likelihood ratio statistic under a mean-shifted outlier detection model is also available. This article offers a practical tutorial for the boutliers package, illustrated with an application to a meta-analysis of chronic low back pain.