There are several generalized linear mixed models to combine direct and indirect evidence on several diagnostic tests from related but independent diagnostic studies simultaneously also known as network meta-analysis. The popularity of these models is due to the attractive features of the normal distribution and the availability of statistical software to obtain parameter estimates. However, modeling the latent sensitivity and specificity using the normal distribution after transformation is neither natural nor computationally convenient. In this article, we develop a meta-analytic model based on the bivariate beta distribution, allowing to obtain improved and direct estimates for the global sensitivities and specificities of all tests involved, and taking into account simultaneously the intrinsic correlation between sensitivity and specificity and the overdispersion due to repeated measures. Using the beta distribution in regression has the following advantages, that the probabilities are modeled in their proper scale rather than a monotonic transform of the probabilities. Secondly, the model is flexible as it allows for asymmetry often present in the distribution of bounded variables such as proportions, which is the case with sparse data common in meta-analysis. Thirdly, the model provides parameters with direct meaningful interpretation since further integration is not necessary to obtain the meta-analytic estimates.