| Affiliation: | 1. Department of Information Statistics, Andong National University, Andong, South Korea;2. Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, Massachusetts;3. Program in Biomedical Radiation Sciences, Department of Transdisciplinary Studies, Graduate School of Convergence Science and Technology, Seoul National University, Seoul, South Korea Biomedical Research Center, Asan Institute for Life Sciences, Asan Medical Center, Seoul, South Korea;4. Department of Statistics, Kyungpook National University, Daegu, South Korea |
| Abstract: | There has been a recent increase in the diagnosis of diseases through radiographic images such as x-rays, magnetic resonance imaging, and computed tomography. The outcome of a radiological diagnostic test is often in the form of discrete ordinal data, and we usually summarize the performance of the diagnostic test using the receiver operating characteristic (ROC) curve and the area under the curve (AUC). The ROC curve will be concave and called proper when the outcomes of the diagnostic test in the actually positive subjects are higher than in the actually negative subjects. The diagnostic test for disease detection is clinically useful when a ROC curve is proper. In this study, we develop a hierarchical Bayesian model to estimate the proper ROC curve and AUC using stochastic ordering in several domains when the outcome of the diagnostic test is discrete ordinal data and compare it with the model without stochastic ordering. The model without stochastic ordering can estimate the improper ROC curve with a nonconcave shape or a hook when the true ROC curve of the population is a proper ROC curve. Therefore, the model with stochastic ordering is preferable over the model without stochastic ordering to estimate the proper ROC curve with clinical usefulness for ordinal data. |
