Is the treatment beneficial? Causal Inference with Ordinal Outcomes: A Bayesian Solution
Abstract
Randomized experiments with ordinal outcomes are common across scientific applications, but conventional causal estimands such as the average treatment effect are difficult to interpret because ordinal categories lack meaningful numerical spacing. Two interpretable estimands, the probabilities that the treatment is beneficial and strictly beneficial, depend on the joint distribution of the potential outcomes and are therefore not identifiable from observed data. The sharp nonparametric bounds used to circumvent this are often too wide to be informative. We develop a Bayesian latent variable framework that models the join distribution by an ordered probit model and delivers coherent super population and finite population posterior inference on both estimands. The association between the potential outcomes remains non-identified and is treated as a sensitivity parameter. We characterize its impact on the estimands theoretically and empirically, showing a non-monotonic relationship governed by the location of the treatment effect relative to the roots of their partial derivatives and use this to recommend a range for applied use. Simulations show that posterior intervals are narrower than the bounds while retaining near-nominal coverage, a gain that reflects the parametric structure imposed rather than additional information in the data. Application on a rheumatoid arthritis trial shows that the method provides precise and practically relevant assessments of treatment effectiveness.
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BibTeX
@misc{dey2026treatment,
title = {{Is the treatment beneficial? Causal Inference with Ordinal Outcomes: A Bayesian Solution}},
author = {Rituparna Dey and Tirthankar Dasgupta},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.23372},
eprint = {2607.23372},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.23372},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Is the treatment beneficial? Causal Inference with Ordinal Outcomes: A Bayesian Solution
AU - Rituparna Dey
AU - Tirthankar Dasgupta
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2607.23372
UR - https://arxiv.org/abs/2607.23372
AB - Randomized experiments with ordinal outcomes are common across scientific applications, but conventional causal estimands such as the average treatment effect are difficult to interpret because ordinal categories lack meaningful numerical spacing. Two interpretable estimands, the probabilities that the treatment is beneficial and strictly beneficial, depend on the joint distribution of the potential outcomes and are therefore not identifiable from observed data. The sharp nonparametric bounds used to circumvent this are often too wide to be informative. We develop a Bayesian latent variable framework that models the join distribution by an ordered probit model and delivers coherent super population and finite population posterior inference on both estimands. The association between the potential outcomes remains non-identified and is treated as a sensitivity parameter. We characterize its impact on the estimands theoretically and empirically, showing a non-monotonic relationship governed by the location of the treatment effect relative to the roots of their partial derivatives and use this to recommend a range for applied use. Simulations show that posterior intervals are narrower than the bounds while retaining near-nominal coverage, a gain that reflects the parametric structure imposed rather than additional information in the data. Application on a rheumatoid arthritis trial shows that the method provides precise and practically relevant assessments of treatment effectiveness.
ER -