  A bivariate copula mixed model has been recently proposed to synthesize
diagnostic test accuracy studies and it has been shown that is superior to the
standard generalized linear mixed model (GLMM) in this context. Here we call
trivariate vine copulas to extend the bivariate meta-analysis of diagnostic
test accuracy studies by accounting for disease prevalence. Our vine copula
mixed model includes the trivariate GLMM as a special case and can also operate
on the original scale of sensitivity, specificity, and disease prevalence. Our
general methodology is illustrated by re-analysing the data of two published
meta-analyses. Our study suggests that there can be an improvement on
trivariate GLMM in fit to data and makes the argument for moving to vine copula
random effects models especially because of their richness including reflection
asymmetric tail dependence, and, computational feasibility despite their
three-dimensionality.
