The accuracy of a diagnostic test, which is often quantified by a pair of measures such as sensitivity and specificity, is critical for medical decision making. Separate studies of an investigational diagnostic test can be combined through meta-analysis; however, such an analysis can be threatened by publication bias. To the best of our knowledge, there is no existing method that accounts for publication bias in the meta-analysis of diagnostic tests involving bivariate outcomes. In this paper, we extend the Copas selection model from univariate outcomes to bivariate outcomes for the correction of publication bias when the probability of a study being published can depend on its sensitivity, specificity, and the associated standard errors. We develop an expectation-maximization algorithm for the maximum likelihood estimation under the proposed selection model. We investigate the finite sample performance of the proposed method through simulation studies and illustrate the method by assessing a meta-analysis of 17 published studies of a rapid diagnostic test for influenza.
Keywords: Copas selection model; diagnostic test accuracy; linear mixed model; meta-analysis; systematic reviews.