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abstract: |
    As the meta-analysis of more than one diagnostic tests can impact clinical decision making and patient health, there is an increasing body of research in models and methods for meta-analysis of diagnostic studies which compare the accuracy of more than one tests. The application of the existing models to compare the accuracy of three or more tests suffers from the curse of multi-dimensionality, i.e., either the number of model parameters increase rapidly or high dimensional integration is required. To overcome these issues in joint meta-analysis of studies comparing $T >2$ diagnostic tests, 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 an one-factor copula that provides flexible reflection asymmetric tail and non-linear dependence. 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.

    **Key Words:** Diagnostic tests; factor copulas; multivariate meta-analysis; mixed models; 