Attributing Cohen's d: Training Data Attribution for Disease-Related Effects in Normative Age Biomarkers

arXiv:2609.07729v1 Announce Type: new Abstract: Normative age models are trained to predict chronological age in a nominally healthy cohort. Applied to patients, they deviate, and the gap between predicted and chronological age is read as disease risk. Here, we attribute the disease-related effect size of the age gap directly to individual training samples, rather than using a prediction-level loss as the attribution target. For Cohen's $d$, the resulting closed-form influence functional, validated against leave-one-out retraining, ranks training samples by their effect on held-out case-control separation. Across four diseases and two biomarker modalities in UK Biobank, removing the 10% most influential training samples raises held-out disease-related effect size in every seed. It more than doubles the metabolomic-age effect for type-2 diabetes and raises the brain-age effect for multiple sclerosis by roughly a third. Random removal leaves effect size flat even at 50% removal, confirming the gain comes from which samples are removed, not how many. Flagged subjects carry subclinical cardiometabolic burden that diagnosis-based exclusion misses, on markers the model never sees. For type-2 diabetes, where the method gains most, the marker recovered is HbA1c, the standard measure of blood sugar control. We release pyinfluence, our influence-function package, for reproducibility and reuse.

Abstract:Normative age models are trained to predict chronological age in a nominally healthy cohort. Applied to patients, they deviate, and the gap between predicted and chronological age is read as disease risk. Here, we attribute the disease-related effect size of the age gap directly to individual training samples, rather than using a prediction-level loss as the attribution target. For Cohen's $d$, the resulting closed-form influence functional, validated against leave-one-out retraining, ranks training samples by their effect on held-out case-control separation. Across four diseases and two biomarker modalities in UK Biobank, removing the 10% most influential training samples raises held-out disease-related effect size in every seed. It more than doubles the metabolomic-age effect for type-2 diabetes and raises the brain-age effect for multiple sclerosis by roughly a third. Random removal leaves effect size flat even at 50% removal, confirming the gain comes from which samples are removed, not how many. Flagged subjects carry subclinical cardiometabolic burden that diagnosis-based exclusion misses, on markers the model never sees. For type-2 diabetes, where the method gains most, the marker recovered is HbA1c, the standard measure of blood sugar control. We release pyinfluence, our influence-function package, for reproducibility and reuse.

Machine Learning (cs.LG); Quantitative Methods (q-bio.QM)

arXiv:2609.07729 [cs.LG]

(or arXiv:2609.07729v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.07729 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Attributing Cohen's d: Training Data Attribution for Disease-Related Effects in Normative Age Biomarkers

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