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To assess the classification accuracy of a continuous diagnostic result, thereceiver operating characteristic (ROC) curve is commonly used in applications.The partial area under the ROC curve (pAUC) is one of widely accepted summarymeasures due to its generality and ease of probability interpretation. In thefield of life science, a direct extension of the pAUC into the time-to-eventsetting can be used to measure the usefulness of a biomarker for diseasedetection over time. Without using a trapezoidal rule, we propose nonparametricestimators, which are easily computed and have closed-form expressions, for thetime-dependent pAUC. The asymptotic Gaussian processes of the estimators areestablished and the estimated variance-covariance functions are provided, whichare essential in the construction of confidence intervals. The finite sampleperformance of the proposed inference procedures are investigated through aseries of simulations. Our method is further applied to evaluate theclassification ability of CD4 cell counts on patient's survival time in theAIDS Clinical Trials Group (ACTG) 175 study. In addition, the inferences can begeneralized to compare the time-dependent pAUCs between patients received theprior antiretroviral therapy and those without it.

Nonparametric Methodology for the Time-Dependent Partial Area under the ROC Curve