Receiver Operating Characteristic (ROC) Curve is used for assessing the ability of a biomarker/screening test to discriminate between non-diseased and diseased subject. In this paper, the parametric ROC curve is studied by assuming two-parameter exponential distribution to the biomarker values. The ROC model developed under this assumption is called bi-exponential ROC (EROC) model. Here, the research interest is to know how far the biomarker will make a distinction between diseased and non-diseased subjects when the gold standard is available using parametric EROC curve and its Area Under the EROC Curve (AUC). Here, the standard error is used as an estimate of the precision of the accuracy measure AUC. The properties of EROC curve that explains the behavior of the EROC curve are also discussed. The AUC along with its asymptotic variance and confidence interval are derived.
The Receiver Operating Characteristic (ROC) curve generated based on assuming a constant shape Bi-Weibull distribution is studied. In the context of ROC curve analysis, it is assumed that biomarker values from controls and cases follow some specific distribution and the accuracy is evaluated by using the ROC model developed from that specified distribution. This article assumes that the biomarker values from the two groups follow Weibull distributions with equal shape parameter and different scale parameters. The ROC model, area under the ROC curve (AUC), asymptotic and bootstrap confidence intervals for the AUC are derived. Theoretical results are validated by simulation studies.
Receiver Operating Characteristics (ROC) curve serves as a statistical tool to measure the quality of Biomarker in 5 accessing the accuracy of any diagnostic test. This paper portrays the historical background of ROC curve and reviews various 6 parametric methods adopted for fitting the ROC curve till date. The parametric ROC models that are considered in this paper 7 are Bi-Normal, Bi-Gamma, Bi-Lomax, Bi-Weibull, Bi-Rayleigh, Bi-Beta, Bi-Triangular, Bi-Uniform and Bi-Exponential ROC 8 models.9
In recent years the ROC curve analysis has got its attention in almost all diversified fields. Basing on the data pattern and its distribution various forms of ROC models have been derived. In this paper, the authors have assumed that the data of two populations (healthy and diseased) follows normal distribution, it is one of the most commonly used forms under parametric approach. The present paper focuses on providing an alternative approach for the tradeoff plot of ROC curve and the computation of AUC using a special function of sigmoid shape called Error function. It is assumed that the test scores of particular biomarker are normally distributed. The entire work has been carried out for providing a new approach for the construction of Binormal ROC curve, which makes use of Error function which can be called as ErROC curve. The summary measure AUC of the resulting ErROC curve has been estimated and defined as ErAUC. The authors have also focused on deriving the expression for obtaining the optimal cut-off point. The new ErROC curve model will provide the true positive rate value at each and every point of false positive rate unlike conventional Binormal ROC model.
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