Abstract
Receiver Operating Characteristic (ROC) Curve is a widely used classification technique in Medical Diagnosis which classifies the healthy and diseased individuals on the basis of optimal cut off value of the biomarker. In this article, we have proposed Constant Shape Weibull Mixture ROC (CSWMROC) model. The properties of CSWMROC Curve are discussed and expressions for AUC, its variance and confidence interval are derived. The estimates of AUC of CSWMROC curve are obtained using Method of Moments (MOM). Numerical example is considered to support the proposed theory.
Highlights
Weibull Mixture distribution is very useful in medical diagnosis because it attains many shapes for different values of shape and scale parameters which helps in modeling different types of data
The optimal cut-off value is defined by the Fluss et al (2005) in the Youden index which is obtained by taking the maximum difference between the CDF of healthy and disease cases
We have proposed Constant Shape Weibull Mixture ROC (CSWMROC) model and found that CSWMROC curve is monotonically increasing, concave in nature and TPR asymmetric
Summary
Weibull Mixture distribution is very useful in medical diagnosis because it attains many shapes for different values of shape and scale parameters which helps in modeling different types of data. Some authors like Newcomb [1886] studied the finite mixture distributions for outlier and Pearson [1894] estimated the parameters of the two component normal-mixture distribution by using the method of moments. Erisoglu and Erisoglu [2014] studied and compared the estimates of the weibull mixture distribution in case of heterogeneous data using EM algorithm, Lmoment method and MLE method. They compared the bias, mean absolute error, total. Pundir and Azharuddin [2014] studied the Exponential Mixture ROC Curve and compared the estimates of AUC of Exponential Mixture ROC Curve using Method of Moments and MLE.
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