A novel robust meta-analysis model using the $t$ distribution for outlier accommodation and detection

TL;DR

This paper introduces a new robust meta-analysis model ($t$Meta) that uses the $t$ distribution to effectively detect and accommodate outliers, offering a simple, efficient, and adaptive approach that outperforms existing methods especially with gross outliers.

Contribution

The paper proposes a novel meta-analysis model ($t$Meta) with a $t$ distribution for effect sizes, enabling simultaneous outlier detection and accommodation with a simple EM algorithm.

Findings

$t$Meta performs well with mild outliers.

$t$Meta remains robust with gross outliers.

Compared to existing methods, $t$Meta offers improved robustness and efficiency.

Abstract

Random effects meta-analysis model is an important tool for integrating results from multiple independent studies. However, the standard model is based on the assumption of normal distributions for both random effects and within-study errors, making it susceptible to outlying studies. Although robust modeling using the $t$ distribution is an appealing idea, the existing work, that explores the use of the $t$ distribution only for random effects, involves complicated numerical integration and numerical optimization. In this paper, a novel robust meta-analysis model using the $t$ distribution is proposed ($t$Meta). The novelty is that the marginal distribution of the effect size in $t$Meta follows the $t$ distribution, enabling that $t$Meta can simultaneously accommodate and detect outlying studies in a simple and adaptive manner. A simple and fast EM-type algorithm is developed for maximum likelihood estimation. Due to the mathematical tractability of the $t$ distribution, $t$Meta frees from numerical integration and allows for efficient optimization. Experiments on real data demonstrate that $t$Meta is compared favorably with related competitors in situations involving mild outliers. Moreover, in the presence of gross outliers, while related competitors may fail, $t$Meta continues to perform consistently and robustly.