一种随机和 Wilcoxon 统计量及其在 ROC 和 LROC 数据分析中的应用。
A random-sum Wilcoxon statistic and its application to analysis of ROC and LROC data.
作者信息
Tang Liansheng Larry, Balakrishnan N
机构信息
Department of Statistics, George Mason University, Fairfax, VA 22030, USA.
出版信息
J Stat Plan Inference. 2011 Jan 1;141(1):335-344. doi: 10.1016/j.jspi.2010.06.011. Epub 2010 Jun 12.
Abstract
The Wilcoxon-Mann-Whitney statistic is commonly used for a distribution-free comparison of two groups. One requirement for its use is that the sample sizes of the two groups are fixed. This is violated in some of the applications such as medical imaging studies and diagnostic marker studies; in the former, the violation occurs since the number of correctly localized abnormal images is random, while in the latter the violation is due to some subjects not having observable measurements. For this reason, we propose here a random-sum Wilcoxon statistic for comparing two groups in the presence of ties, and derive its variance as well as its asymptotic distribution for large sample sizes. The proposed statistic includes the regular Wilcoxon rank-sum statistic. Finally, we apply the proposed statistic for summarizing location response operating characteristic data from a liver computed tomography study, and also for summarizing diagnostic accuracy of biomarker data.
摘要
威尔科克森-曼-惠特尼统计量通常用于两组的无分布比较。使用该统计量的一个要求是两组的样本量固定。在一些应用中，如医学成像研究和诊断标志物研究，这一要求会被违反；在前者中，违反是因为正确定位的异常图像数量是随机的，而在后者中，违反是由于一些受试者没有可观测的测量值。因此，我们在此提出一种随机和威尔科克森统计量，用于在存在 ties 的情况下比较两组，并推导其方差以及大样本量时的渐近分布。所提出的统计量包括常规的威尔科克森秩和统计量。最后，我们将所提出的统计量应用于总结肝脏计算机断层扫描研究中的位置响应操作特征数据，以及总结生物标志物数据的诊断准确性。
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本文引用的文献
1
Maximum likelihood ratio tests for comparing the discriminatory ability of biomarkers subject to limit of detection.用于比较受检测限影响的生物标志物鉴别能力的最大似然比检验。
Biometrics. 2008 Sep;64(3):895-903. doi: 10.1111/j.1541-0420.2007.00941.x. Epub 2007 Nov 19.
2
Receiver operating characteristic curve inference from a sample with a limit of detection.基于具有检测限的样本推断接收器操作特征曲线
Am J Epidemiol. 2007 Feb 1;165(3):325-33. doi: 10.1093/aje/kwk011. Epub 2006 Nov 16.
3
On the Asymptotic Distribution of the Sum of a Random Number of Random Variables.关于随机个数随机变量之和的渐近分布
Proc Natl Acad Sci U S A. 1948 Apr;34(4):162-3. doi: 10.1073/pnas.34.4.162.
4
High-performance wavelet compression for mammography: localization response operating characteristic evaluation.用于乳腺钼靶成像的高性能小波压缩：定位响应操作特征评估。
Radiology. 2006 Jan;238(1):62-73. doi: 10.1148/radiol.2381040896.
5
ROC analysis for markers with mass at zero.对质量为零的标志物进行ROC分析。
Stat Med. 2006 Feb 28;25(4):623-38. doi: 10.1002/sim.2301.
6
Unified measurement of observer performance in detecting and localizing target objects on images.在图像上检测和定位目标物体时观察者表现的统一测量。
Med Phys. 1996 Oct;23(10):1709-25. doi: 10.1118/1.597758.
7
The meaning and use of the area under a receiver operating characteristic (ROC) curve.接受者操作特征（ROC）曲线下面积的意义及应用。
Radiology. 1982 Apr;143(1):29-36. doi: 10.1148/radiology.143.1.7063747.
8
Maximum likelihood analysis of free-response receiver operating characteristic (FROC) data.
Med Phys. 1989 Jul-Aug;16(4):561-8. doi: 10.1118/1.596358.
9
Receiver operator characteristic (ROC) curves and non-normal data: an empirical study.接受者操作特征（ROC）曲线与非正态数据：一项实证研究。
Stat Med. 1990 Mar;9(3):325-37. doi: 10.1002/sim.4780090315.
10
Free-response methodology: alternate analysis and a new observer-performance experiment.自由反应方法：替代分析与一项新的观察者表现实验。
Radiology. 1990 Mar;174(3 Pt 1):873-81. doi: 10.1148/radiology.174.3.2305073.
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