Estimating conditional Mann-Whitney effects using pseudo-observation-based regression

TL;DR

This paper introduces a distribution-free regression model for estimating the Mann-Whitney effect with covariates, using pseudo-observations and bootstrap tests, applicable to ordinal and censored time-to-event data.

Contribution

It develops a novel pseudo-observation-based regression approach for the Mann-Whitney effect, including inference procedures and application to clinical trial data.

Findings

The proposed method provides consistent, asymptotically normal estimates.

Bootstrap tests perform comparably to Cox regression z-tests in simulations.

Applied to breast cancer trial data for progression-free survival analysis.

Abstract

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.