Diagnostic test accuracy studies frequently report on sensitivities and specificities for more than one threshold of the diagnostic test under study. Although it is obvious that the information from all thresholds should be used for a meta-analysis, in practice, frequently, only a single pair of sensitivity and specificity is selected. To overcome this disadvantage, we recently proposed a statistical model for the meta-analysis of such full receiver operating characteristic (ROC) curves that uses the relationship between a ROC curve and a bivariate model for interval-censored data. In this model, diagnostic tests values reported by the single studies were assumed to follow a parametric distribution. We propose a generalization of this model that allows for a flexible semiparametric modelling of the underlying distribution of the diagnostic test values by using the idea of piecewise constant hazard modelling. We show the results of a simulation study that indicates that the approach works reasonably well in practice. Finally, we illustrate the model by the example of population-based screening for type 2 diabetes mellitus.