Bridge-Anchored Partial Identification of a Target Mean under Outcome-Model Drift
Abstract
Transporting an outcome relationship from a source population to a target population where the outcome is unobserved requires the conditional outcome law to be stable across populations. When it is not (outcome-model drift), the target mean is not point-identified and existing transportability estimators are biased. We study settings, common in cross-cohort educational and biomedical data integration, in which bridge outcomes are recorded in both populations and can be expected to drift alongside the target outcome. The bridge splits the drift into a component it can detect, fixed by a bridge-matching equation, and a residual orthogonal to the bridge that no observed quantity restricts. Because the target is a mean, the residual acts through a single scalar sensitivity parameter κ. We prove that the identified set has a closed-form irreducible core, whose width is governed by the residual bound and by how much of the outcome the bridge leaves unexplained, and that its center is first-order invariant to the residual. These results hold for any working exponential family, with point identification arising only as the κ=0 benchmark. We develop a debiased, drift-augmented estimator that is semiparametrically efficient at anchored sensitivity, doubly robust conditional on the bridge-identified drift, and yields rate-robust Imbens-Manski inference for the set. Unlike a bridge-blind sensitivity analysis, which must bound the entire drift channel, the proposed analysis bounds only its bridge-orthogonal part. Simulations confirm that the drift estimator is unbiased under co-drift, that the core width follows its closed form, and that the set fails visibly once the residual bound is exceeded. The motivating setting is the integration of two survey cohorts whose kindergarten mathematics outcome is available in only one.
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BibTeX
@misc{lee2026bridgeanchored,
title = {{Bridge-Anchored Partial Identification of a Target Mean under Outcome-Model Drift}},
author = {Danhyang Lee and Shinyoung Jeon and Shu Yang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36132},
eprint = {2609.36132},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36132},
}
RIS
TY - UNPB
TI - Bridge-Anchored Partial Identification of a Target Mean under Outcome-Model Drift
AU - Danhyang Lee
AU - Shinyoung Jeon
AU - Shu Yang
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.36132
UR - https://arxiv.org/abs/2609.36132
AB - Transporting an outcome relationship from a source population to a target population where the outcome is unobserved requires the conditional outcome law to be stable across populations. When it is not (outcome-model drift), the target mean is not point-identified and existing transportability estimators are biased. We study settings, common in cross-cohort educational and biomedical data integration, in which bridge outcomes are recorded in both populations and can be expected to drift alongside the target outcome. The bridge splits the drift into a component it can detect, fixed by a bridge-matching equation, and a residual orthogonal to the bridge that no observed quantity restricts. Because the target is a mean, the residual acts through a single scalar sensitivity parameter κ. We prove that the identified set has a closed-form irreducible core, whose width is governed by the residual bound and by how much of the outcome the bridge leaves unexplained, and that its center is first-order invariant to the residual. These results hold for any working exponential family, with point identification arising only as the κ=0 benchmark. We develop a debiased, drift-augmented estimator that is semiparametrically efficient at anchored sensitivity, doubly robust conditional on the bridge-identified drift, and yields rate-robust Imbens-Manski inference for the set. Unlike a bridge-blind sensitivity analysis, which must bound the entire drift channel, the proposed analysis bounds only its bridge-orthogonal part. Simulations confirm that the drift estimator is unbiased under co-drift, that the core width follows its closed form, and that the set fails visibly once the residual bound is exceeded. The motivating setting is the integration of two survey cohorts whose kindergarten mathematics outcome is available in only one.
ER -