Department of Biostatistics, Epidemiology and Environmental Health Sciences, Georgia Southern University, Statesboro, Georgia, USA.
Department of Biostatistics, University at Buffalo, Buffalo, New York, USA.
Pharm Stat. 2021 May;20(3):657-674. doi: 10.1002/pst.2099. Epub 2021 Jan 29.
In the receiver operating characteristic (ROC) analysis, the area under the ROC curve (AUC) serves as an overall measure of diagnostic accuracy. Another popular ROC index is the Youden index (J), which corresponds to the maximum sum of sensitivity and specificity minus one. Since the AUC and J describe different aspects of diagnostic performance, we propose to test if a biomarker beats the pre-specified targeting values of AUC and J simultaneously with H : AUC ≤ AUC or J ≤ J against H : AUC > AUC and J > J . This is a multivariate order restrictive hypothesis with a non-convex space in H , and traditional likelihood ratio-based tests cannot apply. The intersection-union test (IUT) and the joint test are proposed for such test. While the IUT test independently tests for the AUC and the Youden index, the joint test is constructed based on the joint confidence region. Findings from the simulation suggest both tests yield similar power estimates. We also illustrated the tests using a real data example and the results of both tests are consistent. In conclusion, testing jointly on AUC and J gives more reliable results than using a single index, and the IUT is easy to apply and have similar power as the joint test.
在受试者工作特征（ROC）分析中，ROC 曲线下面积（AUC）作为诊断准确性的整体衡量指标。另一个流行的 ROC 指标是约登指数（J），它对应于灵敏度和特异性之和的最大值减去 1。由于 AUC 和 J 描述了诊断性能的不同方面，我们建议使用 H ：AUC≤AUC 或 J≤J 来检验生物标志物是否同时优于 AUC 和 J 的预定目标值，其中 H ：AUC>AUC 和 J>J。这是一个具有非凸空间的多元序限制假设，传统的似然比检验无法适用。为此提出了交集-并集检验（IUT）和联合检验。虽然 IUT 检验分别对 AUC 和约登指数进行检验，但联合检验是基于联合置信区间构建的。模拟研究结果表明，两种检验的功效估计值相似。我们还使用实际数据示例说明了这两种检验，并且两种检验的结果都是一致的。总之，同时对 AUC 和 J 进行检验比使用单个指标提供更可靠的结果，并且 IUT 易于应用，其功效与联合检验相似。
