jointly meta-analyses the study-estimates of sensitivity and specificity for the case of a single test, to the case of two tests. They modelled the transformed study-estimates of TPR and FPR of the two tests using a quadrivariate normal distribution, with the information on the agreement between the two tests incorporated in the calculation of the within-study covariance matrix which is assumed fixed.

As the information on the agreement between the two tests is usually not available from all the primary studies, proposed a model that is solely based on the information from the two (one per test) $2\times2$ tables with the number of true positives, true negatives, false negatives and false positives per study. They extended the bivariate generalized mixed model (GLMM) proposed by to the quadrivariate case. The proposed quadrivariate GLMM assumes that the true positives and true negatives from the two tests are conditionally independent and binomially distributed given the bivariate latent pairs of transformed sensitivity and specificity, which are quadrivariate normally distributed. [@nikoloulopoulos-2018-smmr] generalised the quadrivariate GLMM by proposing a model that instead links the four random effects using a quadrivariate D-vine copula rather than the quadrivariate normal distribution.

However, for a particular disease there may be 