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

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 Sensitivity analysis provides a flexible method to address PB and to examine the impact of unpublished studies.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.