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In the setting of survival analysis, the time-dependent area under the receiver operating characteristic curve (AUC) has been proposed as a discrimination measure of interest. In contrast with the diagnostic setting, the definitions of time-dependent sensitivity and specificity are required. This paper evaluates the time-dependent profile of the resulting AUC(t), which has not been previously assessed. We show that, even when the effect of a binary biomarker on the hazard rate is constant, the value of AUC(t) varies over time according to the prevalence of the marker. The Time-profile of the continuous biomarker is illustrated with numerical integration, and data on several prognostic factors in AML are examined.

Time Profile of Time-Dependent Area Under the ROC Curve for Survival Data