Perkins Neil J, Schisterman Enrique F, Vexler Albert
Division of Epidemiology, Statistics, and Prevention Research, National Institute of Child Health and Human Development, National Institutes of Health, Department of Health and Human Services, Bethesda, MD, USA.
Am J Epidemiol. 2007 Feb 1;165(3):325-33. doi: 10.1093/aje/kwk011. Epub 2006 Nov 16.
The receiver operating characteristic curve is a commonly used tool for evaluating biomarker usefulness in clinical diagnosis of disease. Frequently, biomarkers being assessed have immeasurable or unreportable samples below some limit of detection. Ignoring observations below the limit of detection leads to negatively biased estimates of the area under the curve. Several correction methods are suggested in the areas of mean estimation and testing but nothing regarding the receiver operating characteristic curve or its summary measures. In this paper, the authors show that replacement values below the limit of detection, including those suggested, result in the same biased area under the curve when properly accounted for, but they also provide guidance on the usefulness of these values in limited situations. The authors demonstrate maximum likelihood techniques leading to asymptotically unbiased estimators of the area under the curve for both normally and gamma distributed biomarker levels. Confidence intervals are proposed, the coverage probability of which is scrutinized by simulation study. An example using polychlorinated biphenyl levels to classify women with and without endometriosis illustrates the potential benefits of these methods.
受试者工作特征曲线是评估生物标志物在疾病临床诊断中有用性的常用工具。通常，所评估的生物标志物在某些检测限以下存在无法测量或无法报告的样本。忽略检测限以下的观测值会导致曲线下面积的估计出现负偏差。在均值估计和检验领域提出了几种校正方法，但关于受试者工作特征曲线或其汇总指标却没有相关方法。在本文中，作者表明，检测限以下的替代值，包括那些已提出的值，在适当考虑时会导致相同的曲线下偏差面积，但他们也为这些值在有限情况下的有用性提供了指导。作者展示了最大似然技术，该技术可得出正态分布和伽马分布生物标志物水平下曲线下面积的渐近无偏估计量。提出了置信区间，并通过模拟研究仔细审查了其覆盖概率。一个使用多氯联苯水平对患有和未患有子宫内膜异位症的女性进行分类的例子说明了这些方法的潜在益处。
