Meta-analysis is commonly used to synthesize multiple results from individual studies. However, its validation is usually threatened by publication bias and between-study heterogeneity, which can be captured by the Copas selection model. Existing inference methods under this model are all based on conditional likelihood and may not be fully efficient. In this paper, we propose a full likelihood approach to meta-analysis by integrating the conditional likelihood and a marginal semi-parametric empirical likelihood under a Copas-like selection model. We show that the maximum likelihood estimators (MLE) of all the underlying parameters have a jointly normal limiting distribution, and the full likelihood ratio follows an asymptotic central chi-square distribution. Our simulation results indicate that compared with the conditional likelihood method, the proposed MLEs have smaller mean squared errors and the full likelihood ratio confidence intervals have more accurate coverage probabilities. A real data example is analyzed to show the advantages of the full likelihood method over the conditional likelihood method.

荟萃分析通常用于综合单个研究的多个结果。但是，其验证通常受到出版偏倚和研究之间异质性的威胁，这可以由Copas选择模型捕获。在该模型下，现有的推理方法都是基于条件似然的，因此可能并非完全有效。在本文中，我们通过在类似Copas的选择模型下整合条件似然和边际半参数经验似然，提出了一种全似然方法进行荟萃分析。我们表明，所有基础参数的最大似然估计量（MLE）具有共同的正态极限分布，并且全部似然比遵循渐近中心卡方分布。我们的仿真结果表明，与条件似然法相比，提出的MLE具有较小的均方误差，并且全部似然比置信区间具有更准确的覆盖概率。分析了一个真实的数据示例，以显示全似然法相对于条件似然法的优势。