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.

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