[EDGE] A grouped calibration test for logistic regression that tolerates a few corrupted records
Abstract
The Hosmer-Lemeshow calibration test groups patients by predicted risk for a valid reference and loses power that more groups cannot recover. Later tests weight each record's residual alone, which makes them fragile: on an otherwise correct model, one record in a thousand with a corrupted covariate raises the false-alarm rate of Stukel's score test from 5% to 12%, and ten to 63%. Pooling on equal-size groups bounds a wrong record's influence, dividing its residual by its groupmates' variance; without pooling, the same directions are as fragile as Stukel's test after a refit. EDGE, the test proposed here, projects the grouped residuals onto a small basis of calibration shapes. Its degrees of freedom do not depend on the number of groups, so the partition becomes a setting, fine-grained for power and coarse when records may be wrong, and its reference needs no resampling. In a prespecified simulation EDGE was comparable in power to Stukel's test on clean data and 0.064 more powerful on average than the ten-group Hosmer-Lemeshow test. With one and ten exaggerated covariates in a thousand its false-alarm rates were 0.056 and 0.097, and with ten groups below 0.10 up to about ten exaggerated or five reversed. In external validation, at ten groups, its average power was that of Cox's recalibration test and the GiViTI belt, and its false-alarm rate stayed below 0.10 with ten reversed records in a thousand, where theirs did not. In a 70,000-patient cohort its verdict did not change with the partition.
Related
- Benchmarking Goodness-of-Fit and Calibration Algorithms for Logistic Regression Classifiers: A Large-Scale Simulation Study under Sparse Data
- Scalable Cox Regression via Grouped Risk Sets and Sharper LogSumExp Rates
- Grouped Validation and Conformal Calibration for Clustered Cross-National Data with an Application to Harmonized Learning Outcomes
- Data generation for the logistic regression model under controlled conditions
- A penalized logistic generalized regression estimator
BibTeX
@misc{ebrahim2026edge,
title = {{[EDGE] A grouped calibration test for logistic regression that tolerates a few corrupted records}},
author = {Ebrahim Khaled Ebrahim and Osama Abd El-Aziz Hussein and Ahmed El-Kotory},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.20511},
eprint = {2608.20511},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.20511},
}
RIS
TY - UNPB
TI - [EDGE] A grouped calibration test for logistic regression that tolerates a few corrupted records
AU - Ebrahim Khaled Ebrahim
AU - Osama Abd El-Aziz Hussein
AU - Ahmed El-Kotory
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2608.20511
UR - https://arxiv.org/abs/2608.20511
AB - The Hosmer-Lemeshow calibration test groups patients by predicted risk for a valid reference and loses power that more groups cannot recover. Later tests weight each record's residual alone, which makes them fragile: on an otherwise correct model, one record in a thousand with a corrupted covariate raises the false-alarm rate of Stukel's score test from 5% to 12%, and ten to 63%. Pooling on equal-size groups bounds a wrong record's influence, dividing its residual by its groupmates' variance; without pooling, the same directions are as fragile as Stukel's test after a refit. EDGE, the test proposed here, projects the grouped residuals onto a small basis of calibration shapes. Its degrees of freedom do not depend on the number of groups, so the partition becomes a setting, fine-grained for power and coarse when records may be wrong, and its reference needs no resampling. In a prespecified simulation EDGE was comparable in power to Stukel's test on clean data and 0.064 more powerful on average than the ten-group Hosmer-Lemeshow test. With one and ten exaggerated covariates in a thousand its false-alarm rates were 0.056 and 0.097, and with ten groups below 0.10 up to about ten exaggerated or five reversed. In external validation, at ten groups, its average power was that of Cox's recalibration test and the GiViTI belt, and its false-alarm rate stayed below 0.10 with ten reversed records in a thousand, where theirs did not. In a 70,000-patient cohort its verdict did not change with the partition.
ER -