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

TL;DR

This paper introduces nonparametric estimators for the time-dependent partial AUC of ROC curves, providing a practical tool for evaluating biomarkers over time with confidence intervals, demonstrated through AIDS clinical trial data.

Contribution

It proposes a novel nonparametric method for estimating the time-dependent pAUC without trapezoidal approximation, including asymptotic properties and variance estimation.

Findings

Estimators have closed-form expressions and are easily computed.

Simulation studies show good finite-sample performance.

Application to AIDS data demonstrates practical utility.

Abstract

To assess the classification accuracy of a continuous diagnostic result, the receiver operating characteristic (ROC) curve is commonly used in applications. The partial area under the ROC curve (pAUC) is one of widely accepted summary measures due to its generality and ease of probability interpretation. In the field of life science, a direct extension of the pAUC into the time-to-event setting can be used to measure the usefulness of a biomarker for disease detection over time. Without using a trapezoidal rule, we propose nonparametric estimators, which are easily computed and have closed-form expressions, for the time-dependent pAUC. The asymptotic Gaussian processes of the estimators are established and the estimated variance-covariance functions are provided, which are essential in the construction of confidence intervals. The finite sample performance of the proposed inference procedures are investigated through a series of simulations. Our method is further applied to evaluate the classification ability of CD4 cell counts on patient's survival time in the AIDS Clinical Trials Group (ACTG) 175 study. In addition, the inferences can be generalized to compare the time-dependent pAUCs between patients received the prior antiretroviral therapy and those without it.