# 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 called tMeta that uses the t distribution to handle and detect outlying studies more effectively than existing methods.

## Contribution

The novelty is a simple and adaptive model where the marginal effect size follows a t distribution, avoiding numerical integration and enabling robust outlier handling.

## Key findings

- tMeta performs favorably compared to competitors in the presence of mild outliers.
- tMeta remains consistent and robust even when gross outliers are present.
- The model uses a fast EM-type algorithm for maximum likelihood estimation.

## 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 article, a novel robust meta-analysis model using the t distribution is proposed (tMeta). The novelty is that the marginal distribution of the effect size in tMeta follows the t distribution, enabling that tMeta 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, tMeta frees from numerical integration and allows for efficient optimization. Experiments on real data demonstrate that tMeta is compared favorably with related competitors in situations involving mild outliers. Moreover, in the presence of gross outliers, while related competitors may fail, tMeta continues to perform consistently and robustly.