Li Caixia, Lu Ying
Department of Radiology and Biomedical Imaging, University of California, San Francisco, 94143-0946, USA.
Biom J. 2010 Jun;52(3):417-35. doi: 10.1002/bimj.200900228.
Multiple diagnostic tests and risk factors are commonly available for many diseases. This information can be either redundant or complimentary. Combining them may improve the diagnostic/predictive accuracy, but also unnecessarily increase complexity, risks, and/or costs. The improved accuracy gained by including additional variables can be evaluated by the increment of the area under (AUC) the receiver-operating characteristic curves with and without the new variable(s). In this study, we derive a new test statistic to accurately and efficiently determine the statistical significance of this incremental AUC under a multivariate normality assumption. Our test links AUC difference to a quadratic form of a standardized mean shift in a unit of the inverse covariance matrix through a properly linear transformation of all diagnostic variables. The distribution of the quadratic estimator is related to the multivariate Behrens-Fisher problem. We provide explicit mathematical solutions of the estimator and its approximate non-central F-distribution, type I error rate, and sample size formula. We use simulation studies to prove that our new test maintains prespecified type I error rates as well as reasonable statistical power under practical sample sizes. We use data from the Study of Osteoporotic Fractures as an application example to illustrate our method.
多种诊断测试和风险因素通常可用于许多疾病。这些信息可能是冗余的，也可能是互补的。将它们结合起来可能会提高诊断/预测准确性，但也会不必要地增加复杂性、风险和/或成本。通过纳入额外变量所获得的准确性提高，可以通过比较包含和不包含新变量时接收者操作特征曲线下面积（AUC）的增量来评估。在本研究中，我们推导了一个新的检验统计量，以便在多元正态性假设下准确有效地确定这种增量AUC的统计显著性。我们的检验通过对所有诊断变量进行适当的线性变换，将AUC差异与逆协方差矩阵单位中标准化均值偏移的二次形式联系起来。二次估计量的分布与多元贝伦斯 - 费希尔问题相关。我们提供了估计量的显式数学解及其近似非中心F分布、I型错误率和样本量公式。我们通过模拟研究证明，我们的新检验在实际样本量下保持了预先指定的I型错误率以及合理的统计功效。我们以骨质疏松性骨折研究的数据为例来说明我们的方法。
