Orthogonal Validation-Augmented Cox Regression with Internally Validated Failure Indicators Cross-Fitted Estimation, Risk-Set Linearization, and Validation Design
Abstract
Incomplete adjudication and endpoint misclassification arise when gold-standard event classification is available only for an internal validation sample. With accurate follow-up times and covariates but error-prone event indicators, naive Cox regression can be biased and inverseprobability weighting inefficient. We develop orthogonal validation-augmented Cox (OVAC) regression, a cross-fitted augmented Cox estimator for incomplete failure indicators. OVAC replaces the missing event indicator with a cross-fitted augmented pseudo-event and explicitly retains the first-order contribution from estimating the Cox risk-set mean. The same term emerges from projection of the full-data influence function through the validation mechanism, linking the score expansion to the observed-data efficient influence function. The score exhibits exact product-form nuisance drift, yielding double-robust identification, Neyman orthogonality, and root-n inference under product-rate conditions. In 1,000 R replications, full-variance SE/SD ratios were 0.997 and 0.992, with 95% coverage of 0.955 and 0.948. A 200-replication diagnostic showed that the risk-set term alone was 77.8% and 81.1% of the full-SE magnitude, although covariance cancellation made its net SE effect smaller than 0.3%. In a 250-replication method comparison, OVAC reduced empirical variance by 38.8% and 37.7% relative to IPW. OVAC provides machine-learning-compatible Cox estimation with explicit risk-set linearization, calibrated inference, and validation-design guidance.
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BibTeX
@misc{hait2026orthogonal,
title = {{Orthogonal Validation-Augmented Cox Regression with Internally Validated Failure Indicators Cross-Fitted Estimation, Risk-Set Linearization, and Validation Design}},
author = {Subir Hait},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28839},
eprint = {2608.28839},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28839},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Orthogonal Validation-Augmented Cox Regression with Internally Validated Failure Indicators Cross-Fitted Estimation, Risk-Set Linearization, and Validation Design
AU - Subir Hait
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.28839
UR - https://arxiv.org/abs/2608.28839
AB - Incomplete adjudication and endpoint misclassification arise when gold-standard event classification is available only for an internal validation sample. With accurate follow-up times and covariates but error-prone event indicators, naive Cox regression can be biased and inverseprobability weighting inefficient. We develop orthogonal validation-augmented Cox (OVAC) regression, a cross-fitted augmented Cox estimator for incomplete failure indicators. OVAC replaces the missing event indicator with a cross-fitted augmented pseudo-event and explicitly retains the first-order contribution from estimating the Cox risk-set mean. The same term emerges from projection of the full-data influence function through the validation mechanism, linking the score expansion to the observed-data efficient influence function. The score exhibits exact product-form nuisance drift, yielding double-robust identification, Neyman orthogonality, and root-n inference under product-rate conditions. In 1,000 R replications, full-variance SE/SD ratios were 0.997 and 0.992, with 95% coverage of 0.955 and 0.948. A 200-replication diagnostic showed that the risk-set term alone was 77.8% and 81.1% of the full-SE magnitude, although covariance cancellation made its net SE effect smaller than 0.3%. In a 250-replication method comparison, OVAC reduced empirical variance by 38.8% and 37.7% relative to IPW. OVAC provides machine-learning-compatible Cox estimation with explicit risk-set linearization, calibrated inference, and validation-design guidance.
ER -