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In parametric approach, much work has been done over the years. This approach constitutes robust mathematical structures, where these help in evaluating the performance of a diagnostic test and also enables to assess the effect of covariates in the model. We reviewed some of the recent contributions in this approach. It is noticed that, during a decade of time, many researchers have contributed much in developing the ROC curve model by incorporating the covariate effects, different estimating procedures etc.
James A. Hanley (1988) has proved the robustness of using the bi-normal model to fit the ROC curves. Pepe M. S. (2000) has proposed a General linear model approach for evaluating the ROC form and as well as estimating the AUC. Zang Zheng, Pepe, M. S. (2005) has been introduced a linear regression frame work to evaluate the ROC model by involving the covariate effects on the ROC curves. Fawcett Tom et. al, (2007) studied the non-convex ROC curves and the conditions that can lead to empirical and fitted ROC curves that are not convex.
Metz, C. E. (2010) has proposed a proper bi-normal ROC curve for improving the accuracy. The terminology used for proper bi-normal ROC curve is the ‘hook’. This means that the new defined ROC curve will get boosted at the curvilinear part and provides better accuracy when compared to the conventional form of Binormal ROC curve. Ethan J, et al. (2010) have projected the Comparison of ROC curves on the basis of optimal operating point. Davidov, O., & Nov, Y. (2011) proposed an improved, consistent and asymptotically normally distributed estimator which outperforms the original estimator of Hsieh and Turnball (1996).