The Area under the ROC Curve (AUC) is a common index for evaluating the ability of the biomarkers for classification. In practice, a single biomarker has limited classification ability, so to improve the classification performance, we are interested in combining biomarkers linearly and nonlinearly. In this study, while introducing various types of loss functions, the Ramp AUC method and some of its features are introduced as a statistical model based on the AUC index. The aim of this method is to combine biomarkers in a linear or non-linear manner to improve the classification performance of the biomarkers and minimize the experimental loss function by using the Ramp AUC loss function. As an applicable example, in this study, the data of 378 diabetic patients referred to Ardabil and Tabriz Diabetes Centers in 1393-1394 have been used. RAUC method was fitted to classify diabetic patients in terms of functional limitation, based on the demographic and clinical biomarkers. Validation of the model was assessed using the training and test method. The results in the test dataset showed that the area under the RAUC curve for classification of the patients according to the functional limitation, based on the linear kernel pf biomarkers was 0.81 and with a kernel of the radial base function (RBF) was equal to 1.00. The results indicate a strong nonlinear pattern in the data so that the nonlinear combination of the biomarkers had higher classification performance than the linear combination.

Varying coefficient models are among the most important tools for discovering the dynamic patterns when a fixed pattern does not fit adequately well on the data, due to existing diverse temporal or local patterns. These models are natural extensions of classical parametric models that have achieved great popularity in data analysis with good interpretability. The high flexibility and interpretability of these models have led to use in many real applications. In this paper, after presenting a brief review of varying coefficient models, we use the parameter estimation method using the kernel function and cubic
spline then confidence band and hypothesis testing are investigated. Finally, using the real data of Iran’s inflation rate from 1989 to 2017, we show the application and capabilities of the varying coefficient model in interpreting the results. The main challenge in this application is that the panel or longitudinal models or even time series models with heterogeneous variances such as ARCH and GARCH models and their derived models did not fit adequately well on this dataset which justifies the use of varying coefficient models.