Bharat Rajan
Several regression methods based on normal latent variable assumptions had been proposed in the literature that first estimate the parameters of the underlying smooth ROC curve, then estimate the AUC summary measure indirectly, which results in several nuisance parameters and no clear interpretation in terms of the AUC summary measure. Moreover, most commonly used indirect methods do not account for covariate information and fail with degenerate data. A new semi-parametric direct regression method for the AUC summary measure based on discrete ROC curve would be presented. In addition to the regression method for the AUC summary measure, a semi-parametric direct regression method to estimate a smooth ROC curve would also be presented. Upon making some additional assumptions, the proposed ROC regression method can be implemented in the presence of degenerate data. Both the AUC and ROC regression methods assumed a certain functional form of the covariates, and a specified monotone link function. Additionally, the ROC regression method also made an assumption on equal cutoff points for the patients with and without the disease. In order to check the functional form and link function, methods based on cumulative residual sums were developed. A generalized Wald test to check the equal cutoff assumption was also developed. Simulation studies using different ROC models were used to compare the new proposed methods with existing methods in terms of integrated bias and integrated mean square error over the entire ROC curve for the direct ROC regression method, and percent bias and percent mean square error for the direct AUC regression method. The methods were applied to the prostate cancer study and the carotid vessel study, to estimate the AUC and smooth ROC curves and study the validity of the estimation and inference procedures.
