Sequential Certification of Threshold Decisions in Rare-Event Risk Prediction
Abstract
Rare clinical outcomes pose a difficulty deeper than ordinary class imbalance: a penalized logistic model can return finite, stable-looking coefficients before the data support a reliable threshold decision. We formulate the accrual question as decision-targeted sequential certification. On a prespecified finite monitoring schedule and target set, asymptotic prediction bands are adjusted for simultaneous coverage, and certification is assessed only among profiles that might be referred, so that a large low-risk majority cannot trigger an uninformative stop. Under the working rare-event logistic model and stated regularity conditions, each certified decision is asymptotically model-conditionally correct with probability at least 1−α over the schedule, and the effective information scales with the number of genuine events. Simulations and a US linked birth/infant-death application illustrate the gap between a model that is merely estimable and one whose decisions are certifiable: the whole-population rule stopped while more than half of referral-relevant profiles remained ambiguous, whereas the decision-targeted rule did not certify by the 300{,}000-birth horizon despite stable temporal validation. Regularization makes a rare-event model estimable but does not substitute for genuine rare-event information.
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BibTeX
@misc{foo2026sequential,
title = {{Sequential Certification of Threshold Decisions in Rare-Event Risk Prediction}},
author = {Hui-Mean Foo and Yuan-chin Ivan Chang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01968},
eprint = {2609.01968},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01968},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Sequential Certification of Threshold Decisions in Rare-Event Risk Prediction
AU - Hui-Mean Foo
AU - Yuan-chin Ivan Chang
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.01968
UR - https://arxiv.org/abs/2609.01968
AB - Rare clinical outcomes pose a difficulty deeper than ordinary class imbalance: a penalized logistic model can return finite, stable-looking coefficients before the data support a reliable threshold decision. We formulate the accrual question as decision-targeted sequential certification. On a prespecified finite monitoring schedule and target set, asymptotic prediction bands are adjusted for simultaneous coverage, and certification is assessed only among profiles that might be referred, so that a large low-risk majority cannot trigger an uninformative stop. Under the working rare-event logistic model and stated regularity conditions, each certified decision is asymptotically model-conditionally correct with probability at least 1−α over the schedule, and the effective information scales with the number of genuine events. Simulations and a US linked birth/infant-death application illustrate the gap between a model that is merely estimable and one whose decisions are certifiable: the whole-population rule stopped while more than half of referral-relevant profiles remained ambiguous, whereas the decision-targeted rule did not certify by the 300{,}000-birth horizon despite stable temporal validation. Regularization makes a rare-event model estimable but does not substitute for genuine rare-event information.
ER -