Estimation and Inference of the Win Ratio for Two Hierarchical Endpoints Subject to Censoring and Missing Data

2026-02-14

AI Summary

Existing methods for estimating win ratios in the presence of censored and missing data on hierarchical endpoints suffer from bias and inefficiency, particularly when dealing with non-survival outcomes or heterogeneous missingness patterns across treatment groups. This work proposes a nonparametric maximum likelihood estimation (NPMLE) approach that, under non-informative censoring and missing-at-random assumptions, leverages all observed data to yield consistent, efficient, and robust estimates of win ratios for two hierarchical endpoints. The method avoids strong parametric assumptions, provides a closed-form asymptotic variance estimator, and is computationally efficient. Its superior performance is demonstrated through extensive simulations and analyses of real-world data from the HEART-FID and ISCHEMIA clinical trials. To facilitate practical adoption, the authors release WinRS, an open-source, user-friendly R package implementing the proposed methodology.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation
• Machine Learning: Multi-instance/Multi-view Learning

Application Category

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

Abstract

The win ratio (WR) is a widely used metric to compare treatments in randomized clinical trials with hierarchically ordered endpoints. Counting-based approaches, such as Pocock's algorithm, are the standard for WR estimation. However, this algorithm treats participants with censored or missing data inadequately, which may lead to biased and inefficient estimates, particularly in the presence of heterogeneous censoring or missing data between treatment groups. Although recent extensions have addressed some of these limitations for hierarchical time-to-event endpoints, no existing methods -- aside from the computationally intensive multiple imputation approach -- can accommodate settings that include non-survival endpoints that are subject to missing data. In this paper, we propose a simple nonparametric maximum likelihood estimator (NPMLE) of WR for two hierarchical endpoints that are subject to censoring and missing data. Our method uses all observed data, avoids strong parametric assumptions, and comes with a closed-form asymptotic variance estimator. We demonstrate its performance using simulation studies and two data examples, based on the HEART-FID and ISCHEMIA trials. The proposed method provides a consistent estimator, improves estimation efficiency, and is robust under non-informative censoring and missing at random (MAR) assumptions, offering a flexible alternative to existing WR estimation methods. A user-friendly R package, WinRS, is available to facilitate implementation.

Problem

• win ratio
• hierarchical endpoints
• censoring
• missing data
• randomized clinical trials

Innovation

• win ratio
• nonparametric maximum likelihood estimator
• hierarchical endpoints
• censoring and missing data
• asymptotic variance