Kang Le, Chen Weijie, Petrick Nicholas A, Gallas Brandon D
Department of Biostatistics, School of Medicine, Virginia Commonwealth University, Richmond, VA, U.S.A.; Division of Imaging, Diagnostics, and Software Reliability, Office of Science and Engineering Laboratories, Center for Devices and Radiological Health, US Food and Drug Administration, Silver Spring, MD, U.S.A.
Stat Med. 2015 Feb 20;34(4):685-703. doi: 10.1002/sim.6370. Epub 2014 Nov 17.
The area under the receiver operating characteristic curve is often used as a summary index of the diagnostic ability in evaluating biomarkers when the clinical outcome (truth) is binary. When the clinical outcome is right-censored survival time, the C index, motivated as an extension of area under the receiver operating characteristic curve, has been proposed by Harrell as a measure of concordance between a predictive biomarker and the right-censored survival outcome. In this work, we investigate methods for statistical comparison of two diagnostic or predictive systems, of which they could either be two biomarkers or two fixed algorithms, in terms of their C indices. We adopt a U-statistics-based C estimator that is asymptotically normal and develop a nonparametric analytical approach to estimate the variance of the C estimator and the covariance of two C estimators. A z-score test is then constructed to compare the two C indices. We validate our one-shot nonparametric method via simulation studies in terms of the type I error rate and power. We also compare our one-shot method with resampling methods including the jackknife and the bootstrap. Simulation results show that the proposed one-shot method provides almost unbiased variance estimations and has satisfactory type I error control and power. Finally, we illustrate the use of the proposed method with an example from the Framingham Heart Study.
当临床结局（真值）为二元变量时，在评估生物标志物时，受试者工作特征曲线下面积常被用作诊断能力的汇总指标。当临床结局为右删失生存时间时，作为受试者工作特征曲线下面积的扩展，Harrell提出了C指数，作为预测生物标志物与右删失生存结局之间一致性的一种度量。在这项工作中，我们研究了两种诊断或预测系统（它们可以是两种生物标志物或两种固定算法）在C指数方面进行统计比较的方法。我们采用基于U统计量的C估计量，其渐近正态分布，并开发了一种非参数分析方法来估计C估计量的方差以及两个C估计量的协方差。然后构建z检验来比较两个C指数。我们通过模拟研究在I型错误率和检验效能方面验证了我们的一次性非参数方法。我们还将我们的一次性方法与包括刀切法和自助法在内的重抽样方法进行了比较。模拟结果表明，所提出的一次性方法提供了几乎无偏的方差估计，并且具有令人满意的I型错误控制和检验效能。最后，我们用弗明汉心脏研究中的一个例子说明了所提出方法的应用。
