Yang Baoying, Hu Xinjie, Qin Gengsheng
Department of Statistics, College of Mathematics, Southwest Jiaotong University, Chengdu, China.
Department of Mathematics and Statistics, Georgia State University, Atlanta, GA, USA.
Stat Methods Med Res. 2025 Aug;34(8):1574-1589. doi: 10.1177/09622802251345343. Epub 2025 May 29.
In receiver operating characteristicROC analysis, the area under the ROC curve (AUC) is a popular one number summary of the discriminatory accuracy of a diagnostic test. AUC measures the overall diagnostic accuracy of a test but fails to account for the effect of covariates when covariates are present and associated with the test results. Adjustment for covariate effects can greatly improve the diagnostic accuracy of a test. In this paper, using information provided by the influence function, empirical likelihood (EL) methods are proposed for inferences of AUC in presence of covariates. For parameters in the AUC regression model, it is shown that the asymptotic distribution of the influence function-based empirical log-likelihood ratio statistic is a standard chi-square distribution. Hence, confidence regions for the regression parameters can be obtained without any variance estimation. Simulation studies are conducted to compare the finite sample performances of the proposed EL based methods with the existing normal approximation (NA) based method in the AUC regression. Simulation results indicate that the bootstrap-calibrated influence function-based empirical likelihood (BIFEL ) confidence region outperforms the NA-based confidence region in terms of coverage probability. We also propose an interval estimation method for the covariate-adjusted AUC based on the BIFEL confidence region. Finally, we illustrate the recommended method with a real prostate-specific antigen data example.
在接收器操作特性（ROC）分析中，ROC曲线下面积（AUC）是诊断测试鉴别准确性的一种常用单值汇总指标。AUC衡量测试的整体诊断准确性，但当存在协变量且其与测试结果相关时，它无法考虑协变量的影响。对协变量效应进行调整可大大提高测试的诊断准确性。本文利用影响函数提供的信息，提出了在存在协变量时对AUC进行推断的经验似然（EL）方法。对于AUC回归模型中的参数，基于影响函数的经验对数似然比统计量的渐近分布是标准的卡方分布。因此，无需任何方差估计即可获得回归参数的置信区域。进行了模拟研究，以比较所提出的基于EL的方法与AUC回归中现有的基于正态近似（NA）的方法的有限样本性能。模拟结果表明，基于自举校准影响函数的经验似然（BIFEL）置信区域在覆盖概率方面优于基于NA的置信区域。我们还基于BIFEL置信区域提出了一种协变量调整后AUC的区间估计方法。最后，我们用一个真实的前列腺特异性抗原数据示例来说明所推荐的方法。
