  Diagnostic test accuracy studies typically report the number of true
positives, false positives, true negatives and false negatives. There usually
exists a negative association between the number of true positives and true
negatives, because studies that adopt less stringent criterion for declaring a
test positive invoke higher sensitivities and lower specificities. A
generalized linear mixed model (GLMM) is currently recommended to synthesize
diagnostic test accuracy studies. We propose a copula mixed model for bivariate
meta-analysis of diagnostic test accuracy studies. Our general model includes
the GLMM as a special case and can also operate on the original scale of
sensitivity and specificity. Summary receiver operating characteristic curves
are deduced for the proposed model through quantile regression techniques and
different characterizations of the bivariate random effects distribution. Our
general methodology is demonstrated with an extensive simulation study and
illustrated by re-analysing the data of two published meta-analyses. Our study
suggests that there can be an improvement on GLMM in fit to data and makes the
argument for moving to copula random effects models. Our modelling framework is
implemented in the package CopulaREMADA within the open source statistical
environment R.
