Influence diagnostics and outlier detection for dose–response meta-analysis

Dose–response meta-analysis is an evidence synthesis method that enables quantitative analyses concerning the dose–response relationships in clinical and epidemiological studies. In practice of dose–response meta-analyses, several studies might have considerably different profiles from the others, known as outliers. The outliers might be influential to change the overall results of the synthesis analyses, and possibly lead to misleading evidence. In this article, we propose influence diagnostics and outlier detection methods for dose–response meta-analysis that can be generically applied to the flexible multilevel models. We present three influence diagnostic measures: (1) study-level multivariate studentized residual, (2) dose group-level studentized residual, and (3) generalized variance ratio statistic of the regression coefficient estimators, for assessing influences of individual studies or groups to the overall results quantitatively. We also provide bootstrap algorithms to quantify statistical uncertainties of these influential statistics to enable more precise statistical evaluations. We applied these new methods to a dose–response meta-analysis of psychopharmacological interventions for major depression. Using the influence diagnostics methods, we detected one phase-3 clinical trial of fluoxetine and we showed the overall efficacy estimate of the antidepressants might be underestimated by involving this possibly outlying study.