A joint meta-analysis framework for the accuracy of two diagnostic tests accounting for varying study designs

Meta-analyses of the accuracy of two diagnostic tests typically assume tests are independent conditional on true disease status. This assumption is often unrealistic and violation leads to biased estimates of the accuracy of tests used in combination. Existing models accounting for conditional dependence require `joint classification' data (results for both tests and the `gold standard' on all participants) from all studies and/or suffer from computational instability.
We propose a Bayesian hierarchical model for joint meta-analysis of the accuracy of two binary tests, modelling conditional dependence through study-specific log-odds ratios. The model accommodates studies that do not report joint classification data. We show how the model extends to accommodate data from varied study designs, including studies without a gold standard and studies with partial verification, without assuming imperfect reference standards are error-free. We demonstrate the framework with two example meta-analyses.
Our modelling framework retains key features of standard diagnostic test accuracy meta-analysis methods, while allowing for conditional dependence. Ignoring conditional dependence yields biased joint accuracy estimates when conditional dependence is substantial. Our parametrisation maintains computational stability and accommodates data from varied study designs, without requiring an initial data imputation step or assuming error-free reference standards in all studies.