A comprehensive study of the theory and application to biomedical research of Reciever Operating Characteristic (ROC) curves has continued. A theory of nonparametric estimation of the area under the ROC has been developed. This can be used to compare two diagnostic tests via ROC area when the data are ordinal categories rather than continuous variables. Also, the theory of ROC curves has been extended to fuzzy data; instead of knowing that a patient is diseased or nondiseased, it is sometimes useful to view the patients disease state to be a continuous variable between zero and one, where zero indicates normal and one indicates diseased. With such data, one can define weighted estimates of sensitivity and specificity and hence the fuzzy ROC curve. The area under the ROC can be calculated easily. This avoids the issue of bias, which is usually introduced when the two groups are not well separated and individuals without clear identification are dropped from the analysis. Work is being extended to the statistical properties of analyses for comparing areas under two fuzzy ROC'S, as well the important problem of restriction to specific sections of the ROC curve (for example, limiting to specificities greater than .5).
