The Mann-Whitney effect is an effect measure for the order of two sample-specific outcome variables. It has the interpretation of a probability and also a connection to the area under the ROC curve. In the literature it has been considered for both ordinal and right-censored time-to-event outcomes. For both cases, the present paper introduces a distribution-free regression model that relates the Mann-Whitney effect to a linear combination of covariates. To fit the model, we develop a pseudo-observation-based procedure yielding consistent and asymptotically normal coefficient estimates. In addition, we propose bootstrap-based hypothesis tests to infer the effects of the covariates on the Mann-Whitney effect. A simulation study on the small-sample behavior of the proposed method demonstrates that the novel hypothesis tests keep up with the z-test of a Cox regression model. The new methods are used to analyze progression-free survival in breast cancer patients enrolled for the randomized phase III SUCCESS-A trial.

翻译：Mann-Whitney效应是衡量两个样本特定结局变量排序关系的效应指标，其含义可解释为概率，且与ROC曲线下面积相关。文献中已将其应用于有序结局和右删失事件时间结局两种情形。针对这两种情形，本文提出了一种无分布假设的回归模型，将Mann-Whitney效应与协变量的线性组合相关联。为拟合该模型，我们开发了基于伪观测的程序，可得到一致且渐近正态的系数估计值。此外，我们提出了基于bootstrap的假设检验方法，用于推断协变量对Mann-Whitney效应的影响。针对小样本行为的模拟研究表明，新提出的假设检验方法与Cox回归模型的z检验性能相当。新方法被用于分析随机III期SUCCESS-A试验中乳腺癌患者的无进展生存期数据。