A two-sample pseudo-observation-based regression approach for the relative treatment effect

2026-01-22

AI Summary

Existing methods struggle to model the influence of covariates on relative treatment effects—defined as the probability that a subject in one group experiences an event before a subject in another—without imposing distributional assumptions, particularly in the presence of ordered or right-censored data. This work proposes the first distribution-free regression framework that links covariates linearly to relative treatment effects via pseudo-observations, coupled with bootstrap-based inference. The approach requires no specific distributional assumptions, accommodates censored data, and retains statistical power comparable to the z-test when the Cox model is correctly specified. Simulation studies demonstrate its high power, and its application to progression-free survival data from the SUCCESS-A breast cancer trial illustrates strong practical utility and robustness.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Calibration & Uncertainty Quantification
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• relative treatment effect
• two-sample comparison
• distribution-free regression
• pseudo-observation
• covariate effect

Innovation

• pseudo-observation
• relative treatment effect
• distribution-free regression
• bootstrap hypothesis test
• right-censored data