A likelihood-based sensitivity analysis for publication bias on the summary receiver operating characteristic in...

In meta-analysis of diagnostic test accuracy, the summary receiver operating characteristic (SROC) curve is a recommended method to summarize the diagnostic capacity of a medical test in the presence of study-specific cutoff values. The SROC curve can be estimated by bivariate modeling of pairs of sensitivity and specificity across multiple diagnostic studies, and the area under the SROC curve (SAUC) gives the aggregate estimate of diagnostic test accuracy. However, publication bias is a major threat to the validity of the estimates. To make inference of the impact of publication bias on the SROC curve or the SAUC, we propose a sensitivity analysis method by extending the likelihood-based sensitivity analysis of Copas. In the proposed method, the SROC curve or the SAUC are estimated by maximizing the likelihood constrained by different values of the marginal probability of selective publication under different mechanisms of selective publication. A cutoff-dependent selection function is developed to model the selective publication mechanism via the $t$ -type statistics or $P$ -value of the linear combination of the logit-transformed sensitivity and specificity from the published studies. It allows us to model selective publication suggested by the funnel plots of sensitivity, specificity, or diagnostic odds ratio, which are often observed in practice. A real meta-analysis of diagnostic test accuracy is re-analyzed to illustrate the proposed method, and simulation studies are conducted to evaluate its performance.