We propose 2 related models for the meta-analysis of diagnostic tests. Both models are based on the bivariate normal distribution for transformed sensitivities and false-positive rates. Instead of using the logit as a transformation for these proportions, we employ the "t"[subscript alpha] family of transformations that contains the log, logit, and (approximately) the complementary log. A likelihood ratio test for the cutoff value problem is developed, and summary receiver operating characteristic (SROC) curves are discussed. Worked examples showcase the methodology. We compare the models to the hierarchical SROC model, which in contrast employs a logit transformation. Data from various meta-analyses are reanalyzed, and the reanalysis indicates a better performance of the models based on the "t"[subscript alpha] transformation. (Contains 7 figures, 9 tables, and 1 footnote.)