three (or more) diagnostic tests developed, where each of the tests is subject to several studies (e.g., @Takwoingi-etal-2013). The extension of the aforementioned models to compare the accuracy of more than two tests suffers from the curse of multi-dimensionality, i.e., either the number of model parameters increase rapidly or high dimensional integration is required.

In this paper to overcome the drawbacks in existing models for the 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 (random) vector of (transformed) sensitivities and specificities. We assume that the same individuals receive all tests, hence the test results are correlated. As a valid statistical model should account for this dependence, for the random effects distribution, we employ an one-factor copula . The one-factor copula can provide flexible reflection asymmetric tail and non-linear dependence as it is a truncated canonical vine copula rooted at the latent variable/factor. [@joeetal10] have shown that by choosing bivariate linking copulas appropriately, vine copulas can have a flexible range of lower/upper tail dependence (dependence among extreme values), and different lower/upper tail dependence parameters for 