Robust inference methods for meta‐analysis involving influential outlying studies

Meta‐analysis is an essential tool to comprehensively synthesize and quantitatively evaluate results of multiple clinical studies in evidence‐based medicine. In many meta‐analyses, the characteristics of some studies might markedly differ from those of the others, and these outlying studies can generate biases and potentially yield misleading results. In this article, we provide effective robust statistical inference methods using generalized likelihoods based on the density power divergence. The robust inference methods are designed to adjust the influences of outliers through the use of modified estimating equations based on a robust criterion, even when multiple and serious influential outliers are present. We provide the robust estimators, statistical tests, and confidence intervals via the generalized likelihoods for the fixed‐effect and random‐effects models of meta‐analysis. We also assess the contribution rates of individual studies to the robust overall estimators that indicate how the influences of outlying studies are adjusted. Through simulations and applications to two recently published systematic reviews, we demonstrate that the overall conclusions and interpretations of meta‐analyses can be markedly changed if the robust inference methods are applied and that only the conventional inference methods might produce misleading evidence. These methods would be recommended to be used at least as a sensitivity analysis method in the practice of meta‐analysis. We have also developed an R package, robustmeta, that implements the robust inference methods.