Generalized Odds for Ordinal Outcomes: A Causal Inference Framework Adjusting for Covariates
Abstract
Background: Generalized Odds (Gen Odds) provide summaries for ordinal outcomes without requiring the proportional odds assumption. However, conventional Gen Odds compares independently drawn treatment and control outcomes and targets a population-level contrast rather than an individual-level contrast. We developed an individual-level causal formulation of Gen Odds and examined its identification. Methods: We defined the Causal Gen Odds using the joint distribution of potential outcomes and identified it under conditional independence of the potential outcomes given baseline covariates. We developed a model-based estimator using nonproportional cumulative logistic regression and introduced an odds-ratio sensitivity parameter to assess departures from conditional independence. We evaluated the estimators through simulations and illustrated them using data from the ACCORD Study. Results: In simulations, the conditional-independence estimator was approximately unbiased with 95.5% confidence interval coverage under conditional independence, but bias and undercoverage increased with residual dependence. When the sensitivity-analysis estimator incorporated the data-generating dependence parameter, bias remained below 0.01 and coverage ranged from 93.7% to 96.1% across examined settings. In the ACCORD Study, the Causal Gen Odds for right-foot pre-tibial edema was 0.909 (95% CI: 0.880 to 0.940) under conditional independence and remained stable across the examined sensitivity range. Conclusions: The Causal Gen Odds provides an individual-level estimand that complements the conventional population-level Gen Odds. This framework enables estimation of this contrast while explicitly assessing its robustness to assumptions about dependence between potential outcomes.
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BibTeX
@misc{huang2026generalized,
title = {{Generalized Odds for Ordinal Outcomes: A Causal Inference Framework Adjusting for Covariates}},
author = {Runnian Huang and Dandan Shi and Lan Liu and Yunjian Yin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19747},
eprint = {2610.19747},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19747},
}
RIS
TY - UNPB
TI - Generalized Odds for Ordinal Outcomes: A Causal Inference Framework Adjusting for Covariates
AU - Runnian Huang
AU - Dandan Shi
AU - Lan Liu
AU - Yunjian Yin
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.19747
UR - https://arxiv.org/abs/2610.19747
AB - Background: Generalized Odds (Gen Odds) provide summaries for ordinal outcomes without requiring the proportional odds assumption. However, conventional Gen Odds compares independently drawn treatment and control outcomes and targets a population-level contrast rather than an individual-level contrast. We developed an individual-level causal formulation of Gen Odds and examined its identification. Methods: We defined the Causal Gen Odds using the joint distribution of potential outcomes and identified it under conditional independence of the potential outcomes given baseline covariates. We developed a model-based estimator using nonproportional cumulative logistic regression and introduced an odds-ratio sensitivity parameter to assess departures from conditional independence. We evaluated the estimators through simulations and illustrated them using data from the ACCORD Study. Results: In simulations, the conditional-independence estimator was approximately unbiased with 95.5% confidence interval coverage under conditional independence, but bias and undercoverage increased with residual dependence. When the sensitivity-analysis estimator incorporated the data-generating dependence parameter, bias remained below 0.01 and coverage ranged from 93.7% to 96.1% across examined settings. In the ACCORD Study, the Causal Gen Odds for right-foot pre-tibial edema was 0.909 (95% CI: 0.880 to 0.940) under conditional independence and remained stable across the examined sensitivity range. Conclusions: The Causal Gen Odds provides an individual-level estimand that complements the conventional population-level Gen Odds. This framework enables estimation of this contrast while explicitly assessing its robustness to assumptions about dependence between potential outcomes.
ER -