An one‐factor copula mixed model for joint meta‐analysis of multiple diagnostic tests

As meta‐analysis of multiple diagnostic tests impacts clinical decision making and patient health, there is an increasing body of research in models and methods for meta‐analysis of studies comparing multiple diagnostic tests. The application of the existing models to compare the accuracy of three or more tests suffers from the curse of multi‐dimensionality, that is, either the number of model parameters increases rapidly or high dimensional integration is required. To overcome these issues in joint meta‐analysis of studies comparing T > 2 diagnostic tests in a multiple tests design with a gold standard, we propose a model that assumes the true positives and true negatives for each test are conditionally independent and binomially distributed given the 2T‐variate latent vector of sensitivities and specificities. For the random effects distribution, we employ a one‐factor copula that provides tail dependence or tail asymmetry. Maximum likelihood estimation of the model is straightforward as the derivation of the likelihood requires bi‐dimensional instead of 2T‐dimensional integration. Our methodology is demonstrated with an extensive simulation study and an application example that determines which is the best test for the diagnosis of rheumatoid arthritis.