Bharat Rajan
Receiver operating characteristic (ROC) curves are commonly used statistical tools to study the classification accuracy of diagnostic tests for ordinal-scale rating data. ROC curves can be estimated using either a discrete or a smooth ROC curve, with latter being preferred. Several methods based on binormal ROC form have been proposed in the literature to estimate a smooth ROC curve. However, most commonly used methods do not work in the presence of covariates, fail with degenerate data, or make strong assumptions. In this paper, we propose a new semi-parametric direct regression method with a general link function to estimate a smooth ROC curve in presence of covariates that works with degenerate data. The area under the curve (AUC) is one of the well-accepted summary measure for assessing the overall accuracy of the ROC curve. Methods currently used, estimate the AUC indirectly by first estimating the parameters of the ROC curve, leading to several nuisance parameters, and loss in efficiency, with no clear interpretation in terms of the AUC. We also propose a new regression for the non-parametric AUC measure of ordinal-scale tests in presence of discrete and continuous covariates, which works even with degenerate datasets. Simulation studies using different ROC models were used to compare the new methods with existing methods in terms of integrated bias and integrated mean square error over the entire ROC curve for the ROC regression, and percent bias and mean square error for the AUC regression. The results from the simulation studies suggest that the proposed methods has smaller bias and mean square error compared to other methods, and works well in the presence of covariates and with degenerate data. The proposed method were applied to the carotid vessel study and staging of prostate cancer study to investigate the effects of covariate on the AUC values and ROC curve.
