Statistical Methods for Assessing Non-Replicable, Outlying, and Influential Studies

Quantitative evidence synthesis has become a central tool for integrating findings across multiple studies, multi-centre trials, and multi-source cohort data. However, the identification and interpretation of non-replicable, outlying, and influential studies remain insufficiently addressed in practice, despite their potential to substantially affect the robustness and credibility of meta-analytic conclusions. In this paper, we clarify the conceptual distinctions between non-replicability, statistical outlyingness, and study influence, emphasizing that these concepts are related but not interchangeable. We then review the standard principles and procedures of model diagnostics for detecting outlying and influential studies in meta-analysis, together with their underlying statistical rationale. Building on recent methodological developments, we further discuss several practical and methodological refinements, including approaches for handling imprecise and correlated sampling variances, robust diagnostic procedures, and graphical tools for facilitating the identification and interpretation of unusual studies. Finally, we summarize recent advances in outlier and influence diagnostics and provide recommendations for the cautious interpretation and evaluation of studies identified as potentially non-replicable, outlying, or influential within meta-analytic frameworks.