A correlated Bayesian rank likelihood approach to multiple ROC curves for endometriosis: A cBRL approach to ROCs

: In analysis of diagnostic data with multiple tests, it is often the case that these tests are correlated. Modeling the correlation explicitly not only produces valid inference results but also enables borrowing of information. Motivated by the Physician Reliability Study (PRS) that investigated the diagnostic performance of physicians in diagnosing endometriosis, we construct a correlated modeling framework to estimate ROC curves and the associated area under the curves. This correlated approach is quite appealing for the PRS data set that suffers from the problem of small sample sizes, as it enables information borrowing between physician groups and sessions. Given that the test scores appear to be non-normal even after logarithm transformation, we use the ranks of the data to conduct likelihood estimation and inference. We use the deviance information criterion to select competing models and conduct simulation studies to assess model performances. In application to the PRS data set, we found that the physicians are not significantly different in their diagnostic performance between groups; however, they are different between the sessions. This suggests that clinical information may play a more important role in physicians' diagnostic performance than their experiences. Our empirical evidence also demonstrates that when using both woman- and physician-specific random effects, the model parameter estimates are much smoother.