The validation of diagnostic test meta-analysis is often threatened by publication bias, which can be commonly characterized by the Copas selection model. Under this model, conventional approaches to diagnostic meta-analysis are based on conditional likelihood. Since they may have efficiency loss, we propose a full likelihood diagnostic meta-analysis method by integrating the usual conditional likelihood and a marginal semi-parametric empirical likelihood. We show that the resulting maximum likelihood estimators (MLEs) have a jointly normal limiting distribution, and the resulting likelihood ratio follows a central chisquare limiting distribution. Our numerical studies indicate that the proposed MLEs often have smaller mean square errors than the conditional likelihood MLEs. The full likelihood ratio interval estimators generally have more accurate coverage probabilities than the conditional-likelihood-based Wald intervals. We re-study two real meta analyses on influenza and mental health respectively for illustration.

诊断测试荟萃分析的有效性通常受到出版偏倚的威胁，通常可以通过Copas选择模型来表征。在该模型下，诊断性荟萃分析的常规方法基于条件似然。由于它们可能会造成效率损失，因此，我们通过综合通常的条件似然和边际半参数经验似然，提出了一种全似然诊断荟萃分析方法。我们表明，结果最大似然估计（MLE）具有共同的正态极限分布，并且结果似然比遵循中心卡方极限分布。我们的数值研究表明，提出的MLE通常比条件似然MLE的均方误差小。与基于条件似然的Wald间隔相比，完全似然比间隔估计器通常具有更准确的覆盖概率。我们分别对流感和心理健康进行了两次真实的荟萃分析，以进行说明。