Department of Statistics and Biostatistics, 504 Hill Center, Busch Campus, 110 Frelinghuysen Road, Piscataway, NJ 08854, USA.
Acad Radiol. 2013 Jul;20(7):883-8. doi: 10.1016/j.acra.2013.03.006. Epub 2013 Apr 28.
Consider a study evaluating the prognostic value of prostate-specific antigen (PSA), in the presence of Gleason score, in differentiating between early and advanced prostate cancer. This data set features subjects divided into two groups (early versus advanced cancer), with one manifest variable (PSA), one covariate (Gleason score), and one stratification variable (hospital, taking three values). We present a nonparametric method for estimating a shift in median PSA score between the two groups, after adjusting for differences in Gleason score and stratifying on hospital. This method can also be extended to cases involving multivariate manifest variable.
Our method uses estimating equations derived from an existing rank-based estimator of the area under the receiver operating characteristic curve (AUC). This existing AUC estimator is adjusted for stratification and for covariates. We use the adjusted AUC estimator to construct a family of tests by shifting manifest variables in one of the treatment groups by an arbitrary constant. The null hypothesis for these tests is that the AUC is half. We report the set of shift values for which the null hypothesis is not rejected as the resulting confidence region.
Simulated data show performance consistent with the distributional approximations used by the proposed methodology. This methodology is applied to two examples. In the first example, the mean difference in PSA levels between advanced and nonadvanced prostate cancer patients is estimated, controlling for Gleason score. In the second example, to assess the degree to which age and baseline tumor size are prognostic factors for breast cancer recurrence, differences in age and tumor size between subjects with recurrent and nonrecurrent breast cancer, stratified on Tamoxifen treatment and adjusting for tumor grade, are estimated.
The proposed methodology provides a nonparametric method for a statistic measuring adjusted AUC to be used to estimate shift between two manifest variables.
考虑一项研究，评估前列腺特异性抗原（PSA）在格利森评分存在的情况下对早期和晚期前列腺癌的预后价值。该数据集的特征是将受试者分为两组（早期与晚期癌症），有一个显变量（PSA），一个协变量（格利森评分）和一个分层变量（医院，有三个值）。我们提出了一种非参数方法，用于在调整格利森评分和按医院分层的基础上，估计两组之间 PSA 评分中位数的变化。这种方法也可以扩展到涉及多变量显变量的情况。
我们的方法使用从现有的基于秩的接收者操作特征曲线（AUC）下面积估计量中导出的估计方程。这个现有的 AUC 估计量是针对分层和协变量进行调整的。我们使用调整后的 AUC 估计量，通过将一个治疗组中的显变量移动任意常数，构造一组检验。这些检验的零假设是 AUC 是一半。我们报告的一组移位值，对于这些值，零假设未被拒绝，作为结果的置信区间。
模拟数据显示，与所提出的方法学使用的分布逼近一致的性能。该方法应用于两个例子。在第一个例子中，控制格利森评分，估计晚期和非晚期前列腺癌患者 PSA 水平之间的平均差异。在第二个例子中，为了评估年龄和基线肿瘤大小对乳腺癌复发的预后因素的程度，估计了在他莫昔芬治疗和调整肿瘤分级的基础上，复发和非复发乳腺癌患者之间的年龄和肿瘤大小的差异。
所提出的方法提供了一种非参数方法，用于测量调整后的 AUC 的统计量，以估计两个显变量之间的变化。
