Estimation and Inference for Win Measures with Multiple Ordinal Endpoints Subject to Missingness
Abstract
Win measures, including the win ratio, win odds, net benefit, and desirability of outcome ranking, are increasingly used in randomized clinical trials with multiple hierarchical ordinal endpoints. In practice, however, one or more component endpoints may have missing data. The standard pairwise-comparison approach, which treats pairs with missing outcomes as ties, can produce biased estimates, even if the data are missing completely at random. Although inverse probability of censoring weighting methods have been developed for censored survival endpoints, corresponding methods for addressing missing hierarchical ordinal endpoints are not yet available. To address this gap, we develop inverse probability weighted (IPW) and augmented IPW (AIPW) estimators for win measures with hierarchical ordinal endpoints subject to missing data, allowing missingness to depend on treatment assignment and baseline covariates. The IPW estimator corrects bias by reweighting complete observed outcomes using joint non-missingness probabilities involved in estimating the joint cell probabilities that define the win measures. The AIPW estimator additionally incorporates outcome modeling, potentially improving estimation precision and achieving double robustness. For inference, we derive closed-form variance estimators for both methods based on influence functions. Simulation studies show that the standard approach can be substantially biased, whereas the proposed IPW and AIPW estimators exhibit small bias and near-nominal coverage under their respective identifying and model conditions. Applications to the SCOUT-CAP and ACTT-1 trials illustrate the practical utility of the proposed methods. An R package WinMO is provided for implementation.
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BibTeX
@misc{liu2026estimation,
title = {{Estimation and Inference for Win Measures with Multiple Ordinal Endpoints Subject to Missingness}},
author = {Yi Liu and Huiman Barnhart and Sean O'Brien and Yuliya Lokhnygina and Roland A. Matsouaka},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.27085},
eprint = {2605.27085},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.27085},
}
RIS
TY - UNPB
TI - Estimation and Inference for Win Measures with Multiple Ordinal Endpoints Subject to Missingness
AU - Yi Liu
AU - Huiman Barnhart
AU - Sean O'Brien
AU - Yuliya Lokhnygina
AU - Roland A. Matsouaka
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2605.27085
UR - https://arxiv.org/abs/2605.27085
AB - Win measures, including the win ratio, win odds, net benefit, and desirability of outcome ranking, are increasingly used in randomized clinical trials with multiple hierarchical ordinal endpoints. In practice, however, one or more component endpoints may have missing data. The standard pairwise-comparison approach, which treats pairs with missing outcomes as ties, can produce biased estimates, even if the data are missing completely at random. Although inverse probability of censoring weighting methods have been developed for censored survival endpoints, corresponding methods for addressing missing hierarchical ordinal endpoints are not yet available. To address this gap, we develop inverse probability weighted (IPW) and augmented IPW (AIPW) estimators for win measures with hierarchical ordinal endpoints subject to missing data, allowing missingness to depend on treatment assignment and baseline covariates. The IPW estimator corrects bias by reweighting complete observed outcomes using joint non-missingness probabilities involved in estimating the joint cell probabilities that define the win measures. The AIPW estimator additionally incorporates outcome modeling, potentially improving estimation precision and achieving double robustness. For inference, we derive closed-form variance estimators for both methods based on influence functions. Simulation studies show that the standard approach can be substantially biased, whereas the proposed IPW and AIPW estimators exhibit small bias and near-nominal coverage under their respective identifying and model conditions. Applications to the SCOUT-CAP and ACTT-1 trials illustrate the practical utility of the proposed methods. An R package WinMO is provided for implementation.
ER -