A likelihood-based sensitivity analysis for addressing publication bias in meta-analysis of diagnostic studies using exact likelihood

TL;DR

This paper introduces a novel likelihood-based sensitivity analysis method using the Copas t-statistics selection model applied to the bivariate binomial model for meta-analysis of diagnostic studies, effectively addressing publication bias especially in sparse data scenarios.

Contribution

It is the first to apply the Copas t-statistics selection model to the bivariate binomial model in diagnostic meta-analysis, improving bias assessment in sparse data contexts.

Findings

The method performs well in real-world meta-analyses.

Simulation studies show improved bias correction.

Enhanced finite sample properties over previous models.

Abstract

Publication bias (PB) poses a significant threat to meta-analysis, as studies yielding notable results are more likely to be published in scientific journals. Sensitivity analysis provides a flexible method to address PB and to examine the impact of unpublished studies. A selection model based on t-statistics to sensitivity analysis is proposed by Copas. This t-statistics selection model is interpretable and enables the modeling of biased publication sampling across studies, as indicated by the asymmetry in the funnel-plot. In meta-analysis of diagnostic studies, the summary receiver operating characteristic curve is an essential tool for synthesizing the bivariate outcomes of sensitivity and specificity reported by individual studies. Previous studies address PB upon the bivariate normal model but these methods rely on the normal approximation for the empirical logit-transformed sensitivity and specificity, which is not suitable for sparse data scenarios. Compared to the bivariate normal model, the bivariate binomial model which replaces the normal approximation in the within-study model with the exact within-study model has better finite sample properties. In this study, we applied the Copas t-statistics selection model to the meta-analysis of diagnostic studies using the bivariate binomial model. To our knowledge, this is the first study to apply the Copas t-statistics selection model to the bivariate binomial model. We have evaluated our proposed method through several real-world meta-analyses of diagnostic studies and simulation studies.