Predicting of the ROC curve generalization with the methods of parametric and NON-parametric and determining of the best threshold points for NON-monotone marker value

In the healthcare field, diagnostic tests are frequently encountered where low or high values are indicative of a disease. The ROC analysis is used for these diagnostic tests that show a monotonous decrease or increase. However, both low and high values of some diagnostic tests are indicative of the disease. The generalized ROC (gROC) analysis should be used for these diagnostic tests that do not show a monotonous decrease or increase. For this purpose, a T4 (Thyroxine) test which is used to diagnose thyroid disease and whose high and low values are indicative of the disease is discussed. In the gROC analysis, two cut-off points, the lower and the upper cut-off point, are determined to define positivity. The gROC curve is obtained by plotting the false-positive rate (1-specificity) versus the true-positive rate (sensitivity) of the test for diseased and healthy individuals at different lower and upper cut-off points of the T4 test. The area under the gROC curve (gAUC) gives the probability that a randomly and independently selected one diseased and one healthy individual are in a correct classification subset. The gROC curve and the area under the gROC curve are obtained by parametric and non-parametric methods according to the data structure of the diagnostic test. The gROC analysis was performed with parametric and non-parametric methods related to the T4 (Thyroxine) test. For the analysis, functions related to the package "movieROC" package in parametric methods and "nsROC" package in non-parametric methods were used in R programming language. When the marker values of patients or healthy individuals do not have a normal distribution, non-parametric methods give better results than parametric methods. In this study, non-parametric methods gave better results because the distribution of the T4 test of the patients did not show a normal distribution. Youden index was used to determine the best cut-off points.