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

TL;DR

This paper introduces a nonparametric maximum likelihood estimator for the win ratio in clinical trials with hierarchical endpoints, effectively handling censored and missing data, and demonstrating improved accuracy and efficiency over existing methods.

Contribution

It proposes a novel NPMLE approach for estimating the win ratio with censored and missing data, including a closed-form variance estimator, and provides practical implementation via an R package.

Findings

The method performs well in simulations under various censoring and missing data scenarios.

It yields consistent and efficient estimates of the win ratio.

Application to real trial data demonstrates practical utility.

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.