Methodology for the Time-Dependent AUC and Its Applications

To evaluate the performance of test results in earlyetection of disease, the receiver operating characteristic (ROC)urves are widely used. The area under the ROC curve (AUC) and theartial area under the ROC curve (PAUC) are the most popular summaryeasures for its generality and ease of probability interpretation.n applications, data with the binary time-varying disease statusre frequently encountered. The cases and controls in the ROCnalysis are more suitable defined over time. A major challenge inealing this issue is that the failure status of some individualsight not be available due to censoring. To further increaselassification ability of multiple biomarkers, research interestssually focus on seeking combinations of these biomarkers with theighest ROC curve.n contrast to the existing methods, we propose nonparametricstimators for the time-dependent AUC and PAUC with explicitxpressions and a rigorous theoretical development for theseethods. Moreover, we use a generalized linear model withime-varying coefficients to characterize the time-dependent AUC as function of covariate values. For the parameter functions and theelated classification accuracies, the estimation and inferencerocedures are also proposed. Under the validity of an extendedeneralized linear model (EGLM) with time-varying coefficients andn unknown link function for the conditional survival distribution,wo nonparametric procedures are proposed to estimate the optimalomposite markers based on the estimation procedures of theime-dependent AUC. Two empirical examples from the AIDS Clinicalrials Group (ACTG) 175 study and the Angiography Coronary Arteryisease (CAD) study are used to illustrate the usefulness of ourethods. Finally, some concluding remarks and further researchopics of interests are devoted in this thesis.