{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19747",
  "author_total": 4,
  "authors": [
    {
      "name": "Runnian Huang"
    },
    {
      "name": "Dandan Shi"
    },
    {
      "name": "Lan Liu"
    },
    {
      "name": "Yunjian Yin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cbevhcxzskz9v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19747",
  "fulltext_url": null,
  "id": "cbevhcxzskz9v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19747",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "2613|Advanced Causal Inference Techniques"
    ]
  ],
  "openalex": "W7222344920",
  "pdf_url": "https://arxiv.org/pdf/2610.19747",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cbevhcxzskz9v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:42Z",
      "native_id": "2610.19747",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19747"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Generalized Odds for Ordinal Outcomes: A Causal Inference Framework Adjusting for Covariates",
  "title_text": "Generalized Odds for Ordinal Outcomes: A Causal Inference Framework Adjusting for Covariates",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:42Z",
  "url": "https://research.draconitic.com/paper/cbevhcxzskz9v",
  "venue": "arXiv",
  "versions": []
}