A Robust Bayesian Copas Selection Model for Quantifying and Correcting Publication Bias

TL;DR

This paper introduces a Bayesian hierarchical model using heavy-tailed distributions to better account for publication bias in meta-analyses, along with a new measure based on Hellinger distance to quantify bias magnitude.

Contribution

It proposes a robust Bayesian Copas selection model with heavy-tailed effects and a novel bias quantification measure, addressing limitations of normality assumptions and enhancing bias assessment.

Findings

Improved bias correction in simulations and real meta-analyses.

Effective quantification of publication bias magnitude.

Application to 1500 Cochrane meta-analyses.

Abstract

The validity of conclusions from meta-analysis is potentially threatened by publication bias. Most existing procedures for correcting publication bias assume normality of the study-specific effects that account for between-study heterogeneity. However, this assumption may not be valid, and the performance of these bias correction procedures can be highly sensitive to departures from normality. Further, there exist few measures to quantify the magnitude of publication bias based on selection models. In this paper, we address both of these issues. First, we explore the use of heavy-tailed distributions for the study-specific effects within a Bayesian hierarchical framework. The deviance information criterion (DIC) is used to determine the appropriate distribution to use for conducting the final analysis. Second, we develop a new measure to quantify the magnitude of publication bias based on Hellinger distance. Our measure is easy to interpret and takes advantage of the estimation uncertainty afforded naturally by the posterior distribution. We illustrate our proposed approach through simulation studies and meta-analyses on lung cancer and antidepressants. To assess the prevalence of publication bias, we apply our method to 1500 meta-analyses of dichotomous outcomes in the Cochrane Database of Systematic Reviews. Our methods are implemented in the publicly available R package RobustBayesianCopas.