Testing for publication bias in meta-analysis under Copas selection model

TL;DR

This paper introduces a new score-based test for detecting publication bias in meta-analyses under the Copas selection model, addressing the lack of rigorous testing procedures and providing a bootstrap method for practical use.

Contribution

We develop a novel test statistic for publication bias detection under the Copas model and derive its distribution, filling a key methodological gap.

Findings

The proposed test performs well in simulations.

It effectively detects publication bias in real meta-analyses.

The bootstrap method provides accurate p-values.

Abstract

In meta-analyses, publication bias is a well-known, important and challenging issue because the validity of the results from a meta-analysis is threatened if the sample of studies retrieved for review is biased. One popular method to deal with publication bias is the Copas selection model, which provides a flexible sensitivity analysis for correcting the estimates with considerable insight into the data suppression mechanism. However, rigorous testing procedures under the Copas selection model to detect bias are lacking. To fill this gap, we develop a score-based test for detecting publication bias under the Copas selection model. We reveal that the behavior of the standard score test statistic is irregular because the parameters of the Copas selection model disappear under the null hypothesis, leading to an identifiability problem. We propose a novel test statistic and derive its limiting distribution. A bootstrap procedure is provided to obtain the p-value of the test for practical applications. We conduct extensive Monte Carlo simulations to evaluate the performance of the proposed test and apply the method to several existing meta-analyses.