The relative treatment 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 or right-censored time-to-event outcomes. For both cases, the present paper introduces a distribution-free regression model that relates the relative treatment 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 relative treatment effect. A simulation study compares the novel method to Cox regression, demonstrating that the proposed hypothesis tests have high power and keep up with the z-test of the Cox model even in scenarios where the latter is specified correctly. The new methods are used to re-analyze data from the SUCCESS-A trial for progression-free survival of breast cancer patients.

翻译：相对治疗效果是衡量两个样本特异性结局变量顺序的一种效应指标，其解释具有概率意义，且与ROC曲线下面积存在关联。现有文献已将其应用于有序分类结局或右删失生存时间结局的分析。针对这两种情况，本文提出了一种与协变量线性组合相关联的无分布回归模型。为拟合该模型，我们开发了基于伪观测的估计程序，该程序能产生具有一致性和渐近正态性的系数估计量。此外，我们提出了基于自助法的假设检验方法，用以推断协变量对相对治疗效果的影响。通过模拟研究将新方法与Cox回归进行比较，结果表明：即使在Cox模型设定正确的情况下，所提出的假设检验方法仍能保持较高检验效能，其性能与Cox模型的z检验相当。最后，我们运用新方法重新分析了SUCCESS-A试验中乳腺癌患者无进展生存期的数据。