A multinomial quadrivariate D-vine copula mixed model for diagnostic studies meta-analysis accounting for non-evaluable subjects
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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. In meta-analysis of diagnostic test accuracy studies, the existence of non-evaluable subjects is an important issue that could potentially lead to biased estimates of diagnostic test accuracy. In this paper we propose a methodology for the meta-analysis of diagnostic tests where we additionally account for non-evaluable outcomes of the diagnostic test. We assume 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 illustrated by meta-analysing diagnostic accuracy studies of coronary computed tomography angiography for the detection of coronary artery disease.
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