Covariate-adjusted win statistics in randomized clinical trials with ordinal outcomes

2025-08-27

AI Summary

In randomized trials with ordinal outcomes (e.g., disease progression grades), conventional ordinal regression suffers from bias when the proportional odds assumption fails or due to non-collapsibility. To address this, we propose a pairwise comparison framework based on the win ratio and win difference, and develop covariate-adjusted, propensity score–weighted U-statistic estimators. We innovatively integrate inverse probability weighting (IPW) with overlap weighting (OW) to construct an enhanced doubly robust estimator that improves efficiency while preserving double robustness. We derive its asymptotic normality and consistent variance estimation, and implement it in the R package *winPSW*. Simulation studies and reanalysis of the ORCHID trial demonstrate that our method substantially outperforms unadjusted estimators, and the enhanced estimator further reduces mean squared error. The approach provides a generalizable, efficient, and robust tool for average treatment effect inference on ordinal outcomes.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Causality
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

Ordinal outcomes are common in clinical settings where they often represent increasing levels of disease progression or different levels of functional impairment. Such outcomes can characterize differences in meaningful patient health states that are directly relevant to clinical researchers and frequently represent composite outcomes that include absorbing states such as death. To compare different intervention strategies in clinical trials, the direct use of ordinal logistic regression models may not be ideal for analyzing ranked outcomes due to non-collapsibility, lack of estimation and clarity, or failure of the common underlying proportional odds assumption. In this article, we focus on representing the average treatment effect for ordinal outcomes via intrinsic pairwise outcome comparisons captured through win estimates, such as the win ratio and win difference. We first develop propensity score weighting estimators, including both inverse probability weighting (IPW) and overlap weighting (OW), tailored to estimating win parameters. Furthermore, we develop augmented weighting estimators that leverage an additional ordinal outcome regression to potentially improve efficiency over weighting alone. Leveraging the theory of U-statistics, we establish the asymptotic theory for all estimators, and derive closed-form variance estimators to support statistical inference. Through extensive simulations we demonstrate the enhanced efficiency of the weighted estimators over the unadjusted estimator, with the augmented weighting estimators showing a further improvement in efficiency except for extreme cases. Finally, we illustrate our proposed methods with the ORCHID trial, and implement our covariate adjustment methods in an R package winPSW to facilitate the practical implementation.

Problem

• Addresses non-collapsibility issues in ordinal outcome analysis
• Develops covariate-adjusted win statistics for clinical trials
• Improves efficiency in estimating treatment effects for ordinal outcomes

Innovation

• Propensity score weighting estimators for win parameters
• Augmented weighting estimators with ordinal outcome regression
• Closed-form variance estimators using U-statistics theory