Bootstrap-Calibrated Outlier Detection and Influence Diagnostics for Meta-Analysis: The R Package boutliers

Meta-analysis is a statistical tool commonly used within systematic reviews to synthesize quantitative evidence, but individual studies with atypical results or disproportionate influence can materially affect pooled estimates, heterogeneity estimates, and the conclusions drawn from evidence syntheses. Conventional outlier and influence diagnostics for meta-analysis are useful, but their interpretation often relies on asymptotic reference values or informal rules of thumb, which may be inadequate when the number of studies is limited or heterogeneity is substantial. We introduce boutliers, an R package that implements bootstrap-calibrated outlier detection and influence diagnostics for fixed-effect and random-effects meta-analysis. The package provides leave-one-study-out diagnostics based on Studentized deleted residuals, relative changes in the variance of the pooled effect estimator, and relative changes in the between-study variance, together with a likelihood-ratio diagnostic based on a mean-shifted model. For each diagnostic measure, bootstrap reference distributions, critical values, and p-values are provided to support quantitative interpretation of influential studies. We describe the statistical framework, implementation, and practical use of the package and illustrate its application using a real published meta-analysis dataset on spinal manipulative therapy for chronic low back pain. The boutliers package provides accessible tools for incorporating uncertainty-calibrated influence diagnostics into routine meta-analytic practice.