Meta-analysis for the comparison of two diagnostic tests-A new approach based on copulas.

Meta-analysis of diagnostic studies is still field of ongoing biometrical research. Especially, clinical researchers call for methods that allow for a comparison of different diagnostic tests to a common gold standard. Focussing on two diagnostic tests, the main parameters of interest are differences of sensitivities and specificities (with their corresponding confidence intervals) between the two diagnostic tests while accounting for the various associations across the two tests and the single studies. Similar to our previous work using generalized linear mixed models to this task, we propose a model with a quadrivariate response consisting of the two sensitivities and the two specificities of both tests. This new approach uses the ideas of copula modelling, and especially a quadrivariate Gaussian copula and a quadrivariate vine copula, which is built from bivariate Plackett copulas. The different copulas are compared in a simulation study and illustrated by the application of population-based screening for type 2 diabetes.