Vine copula mixed models for meta-analysis of diagnostic accuracy studies without a gold standard

Numerous statistical models have been proposed for conducting meta-analysis of diagnostic accuracy studies when a gold standard is available. However, in real-world scenarios, the gold standard test may not be perfect due to several factors such as measurement error, non-availability, invasiveness, or high cost. A generalized linear mixed model (GLMM) is currently recommended to account for an imperfect reference test. We propose vine copula mixed models for meta-analysis of diagnostic test accuracy studies with an imperfect reference standard. Our general models include the GLMM as a special case, can have arbitrary univariate distributions for the random effects, and can provide tail dependencies and asymmetries. Our general methodology is demonstrated with an extensive simulation study and illustrated by insightfully re-analyzing the data of a meta-analysis of the Papanicolaou test that diagnoses cervical neoplasia. Our study suggests that there can be an improvement on GLMM and makes the argument for moving to vine copula random effects models.