Methodology for the Time-dependent AUC and its Applications

Abstract

Disease detection and risk assessment have now been extended from binary disease status to time-dependent disease status. It is desirable, for instance, to know if patients can survive 5 years or not. The time-dependent receiver operating characteristic (ROC) curve analysis is used to accomplish this task, and the most commonly used summary index is the area under the time-dependent ROC curve (the time-dependent AUC). When multiple biomarkers of a subject are available, the one with larger area is usually considered to have better classification ability. Methodology for the time-dependent AUC based on censored survival data thus becomes urgent. In this talk, two related topics will be covered and are described as follows.(a) Traditionally, the time-dependent AUC is calculated by numerical integration of the estimated time-dependent ROC curve and hence, the asymptotic properties and inference procedures are difficult to construct. In view of this problem, nonparametric estimators with explicit expression for the time-dependent AUC are proposed with rigorously developed large sample properties. This facilitates the establishments of statistical inference procedures. Moreover, the performance of a biomarker may depend on other attributes such as age, gender, etc. A generalized linear model for the time-dependent AUC is proposed to evaluate the influence of covariates on the classification ability. The analysis can be applied to decide the appropriate subpopulation where biomarker performs well. (b) Combining multiple biomarkers in order to achieve higher classification ability is another important issue. Based on the extended generalized linear model (EGLM) with unspecified link function, estimators for the optimal composite biomarkers are proposed which can be shown to possess the highest time-dependent ROC curves and therefore, the largest time-dependent AUCs.