  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 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, 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 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 an 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.
