Goodness-of-fit issues in ROC curve estimation

Zhou recently considered goodness-of-fit (GOF) testing for receiver operating characteristic (ROC) curves estimated by applying the binormal and other bidistributional models to rating method data. He interpreted significant GOF tests as evidence that different decision thresholds were applied to diseased and nondiseased subjects and concluded that, in such circumstances, an ROC curve does not exist. In this article the author demonstrates that the GOF test accommodates many alternative hypotheses and that a significant test result need not be equated with an interaction between disease status and decision criteria or with non-existence of an ROC curve. He develops a new family of ROC curves based on a fully parameterized bidistributional model. The family includes the binormal ROC curve, but generalizes its structure by signifying all identifiable deviations in parameters of the latent distributions that define the model. The family provides a unified framework of alternative models to the binormal assumption and of alternative hypotheses to the GOF test for that assumption.