Abstract
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.
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Acknowledgements
The authors thank the Editor, the Associate Editor and an anonymous referee for helpful comments and suggestions that have led to significant improvements in the paper. Dr. Liu’s research was supported by the National Natural Science Foundation of China (11771144, 11971300, 11871287), the State Key Program of the National Natural Science Foundation of China (71931004), the Natural Science Foundation of Shanghai (19ZR1420900, 17ZR1409000), the development fund for Shanghai talents , the 111 project (B14019), and the Fundamental Research Funds for the Central Universities. Dr. Li was supported in part by the Natural Sciences and Engineering Research Council of Canada grant number RGPIN-2015-06592.
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Li, M., Liu, Y., Li, P. et al. Empirical likelihood meta-analysis with publication bias correction under Copas-like selection model. Ann Inst Stat Math 74, 93–112 (2022). https://doi.org/10.1007/s10463-021-00793-4
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DOI: https://doi.org/10.1007/s10463-021-00793-4