Comparing areas under the ROC curve (AUCs) is a popular approach to compare prognostic biomarkers. The aim of this paper is to present an efficient method to control the family-wise error rate when multiple comparisons are performed. We suggest to combine the max-t test and the closed testing procedures. We build on previous work on asymptotic results for ROC curves and on general multiple testing methods to efficiently take into account both the correlations between the test statistics and the logical constraints between the null hypotheses. The proposed method results in an uniformly more powerful procedure than both the single-step max-t test procedure and popular stepwise extensions of the Bonferroni procedure, such as Bonferroni–Holm. As demonstrated in this paper, the method can be applied in most usual contexts, including the time-dependent context with right censored data. We show how the method works in practice through a motivating example where we compare several psychometric scores to predict the t-year risk of Alzheimer's disease. The example illustrates several multiple testing settings and demonstrates the advantage of using the proposed methods over common alternatives. R code has been made available to facilitate the use of the methods by others.

中文翻译：

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对 ROC 曲线下面积进行多重比较的封闭式 max-t 检验

比较 ROC 曲线下面积 (AUC) 是比较预后生物标志物的常用方法。本文的目的是提出一种在进行多重比较时控制全族错误率的有效方法。我们建议将 max-t 测试和封闭测试程序结合起来。我们建立在先前关于 ROC 曲线的渐近结果的工作和一般的多重测试方法的基础上，以有效地考虑测试统计数据之间的相关性和零假设之间的逻辑约束。与单步 max-t 测试过程和 Bonferroni 过程的流行逐步扩展（如 Bonferroni-Holm）相比，所提出的方法产生了一个更强大的过程。正如本文所证明的，该方法可以应用于最常见的情况下，包括具有右删失数据的时间相关上下文。我们通过一个激励性的例子展示了该方法在实践中的工作原理，我们比较了几个心理测量分数来预测阿尔茨海默病的 t 年风险。该示例说明了几种多重测试设置，并展示了使用建议的方法优于常见替代方法的优势。已提供 R 代码以方便其他人使用这些方法。