  Diagnostic test accuracy studies observe the result of a gold standard
procedure that defines the presence or absence of a disease and the result of a
diagnostic test. They typically report the number of true positives, false
positives, true negatives and false negatives. However, diagnostic test
outcomes can also be either non-evaluable positives or non-evaluable negatives.
We propose a novel model for meta-analysis of diagnostic studies in the
presence of non-evaluable outcomes that assumes independent multinomial
distributions for the true and non-evaluable positives, and, the true and non
evaluable negatives, conditional on the latent sensitivity, specificity,
probability of non-evaluable positives and probability of non-evaluable
negatives in each study. For the random effects distribution of the latent
proportions, we employ a drawable vine copula that can successively model the
dependence in the joint tails. Our methodology is demonstrated with an
extensive simulation study and applied to data from diagnostic accuracy studies
of coronary computed tomography angiography for the detection of coronary
artery disease. The comparison of our method with the existing approaches
yields findings in the real data application that change the current
conclusions.
