Empirical likelihood meta analysis with publication bias correction under Copas-like selection model

TL;DR

This paper introduces a full likelihood approach for meta analysis under the Copas-like selection model, improving efficiency and accuracy in the presence of publication bias and heterogeneity.

Contribution

It develops a novel full likelihood method combining conditional and semi-parametric empirical likelihood, enhancing inference in meta analysis with publication bias correction.

Findings

MLEs have a jointly normal limiting distribution

Full likelihood ratio follows an asymptotic chi-square distribution

Proposed method yields smaller MSE and more accurate coverage

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 chisquare 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.