# Bias-corrected Cox regression with AI-extracted covariates via calibration summary statistics

arXiv: https://arxiv.org/abs/2607.25868 · HTML: https://mlsanity.com/paper/2607.25868/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 23 references that are in the map.
- First posted on arXiv 28 Jul 2026.

## Builds on (most cited first, 3 of 3)

- [Prediction-Powered Inference](https://mlsanity.com/paper/2301.09633/) (2023)
- [Assumption-Lean and Data-Adaptive Post-Prediction Inference](https://mlsanity.com/paper/2311.14220/) (2023)
- [Bayesian correction for covariate measurement error: a frequentist evaluation and comparison with regression calibration](https://mlsanity.com/paper/1603.06284/) (2016)

## Abstract (arXiv)

Large-scale observational studies increasingly rely on AI pipelines to extract structured variables from unstructured clinical records. A common workflow separates the data vendor, who validates extraction accuracy with a gold-standard sample, from the downstream researcher, who receives only the extracted dataset and summary accuracy statistics. We develop a bias-correction framework for the Cox proportional hazards model when covariates are subject to AI extraction error. Within a unified multivariate calibration framework, we show that the naive Cox estimator's bias decomposes into a leading-order calibration term and a second-order residual that vanishes as extraction accuracy improves. The leading-order term yields a corrected estimator that operates as a post-hoc matrix multiplication on the output of any standard Cox software. We further derive bias-adjusted confidence intervals that incorporate calibration uncertainty and a sensitivity diagnostic for assessing whether the neglected residual could materially affect inference. Synthetic data experiments with cross-dependent extraction errors and controlled nonlinear calibration violations confirm that the correction substantially reduces bias and achieves near-nominal coverage even under mild violations of the linear calibration assumption. The framework yields a concrete reporting specification: a short list of summary statistics that data vendors should provide alongside any AI-extracted covariate dataset used in survival analysis.