Sensitivity Analysis for Publication Bias in Diagnostic Meta‐Analysis of Sparsity Using the Copas t ‐Statistic Selection Function

Publication bias (PB) poses a significant threat to meta-analysis of diagnostic studies, as studies yielding significant results are more likely to be published in scientific journals, leading to the synthesized diagnostic capacity possibly being overestimated. Sensitivity analysis provides a flexible method to address PB by assuming different proportions of unpublished studies. Most existing methods addressing PB in meta-analysis of diagnostic studies are based on the bivariate normal model using normal approximations. However, they are unsuitable for meta-analysis with sparse data, which is common in diagnostic studies with high sensitivities or specificities. Alternatively, the bivariate binomial model relies on the exact within-study model and has better finite sample properties. To address PB in the bivariate binomial model, we model the selective publication process of diagnostic studies by extending the Copas t-statistic model and propose the likelihood conditional on published and estimation strategies. Our proposal provides an interpretable way to address PB on the summary receiver operating characteristic curve, an essential tool for synthesizing diagnostic accuracy. We show the practicability of the proposed method on several real-world meta-analyses of diagnostic studies and evaluate the performance by simulation studies.