  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.
