Diagnostic accuracy studies often evaluate diagnostic tests at several threshold values, aiming to make recommendations on optimal thresholds for use in practice. Methods for meta-analysis of full receiver operating characteristic (ROC) curves have been proposed but still have deficiencies. We recently proposed a parametric approach that is based on bivariate time-to-event models for interval-censored data to this task. To increase the flexibility of that approach, to cover a wide range of distributions of diagnostic test values and to address the open point of model selection, we here suggest to use the generalized "F" family of distributions that includes previously used distributions for the bivariate time-to-event model as special cases. The results of a simulation study are given as well as an illustration by an example of population-based screening for type 2 diabetes mellitus.