Identity-Corrected Embedding Deltas for Lung-Nodule Progression: A Longitudinal CT Foundation-Embedding Biomarker

Frozen 3D CT foundation models are increasingly used as off-the-shelf feature extractors. For longitudinal imaging, their natural biomarker follows the delta-radiomics paradigm: the element-wise difference between a follow-up and a baseline embedding, which we call the embedding delta. Yet what this delta represents remains poorly understood. Studying index-nodule progression in the National Lung Screening Trial (NLST), we show that the well-localized FMCIB embedding delta is a strong progression biomarker (AUC $0.73$), substantially outperforming a single-timepoint embedding (AUC $0.56$) and its scalar magnitude (AUC $0.64$), which indicates that its predictive signal is not simply a measure of change magnitude or nodule size. We further find that a large and structured component of the embedding delta is a stable, patient-linked factor: a compact subspace recovered from paired longitudinal embeddings re-identifies patients across a one-year interval at $31.7\%$ rank-1 accuracy in a $2{,}166$-patient gallery ($\approx$$690\times$ chance), survives scanner removal (which is consistent with a patient-linked signal rather than an acquisition artifact), and accounts for $37\%$ of the delta variance. Projecting out this identity subspace, without using progression labels, improves progression prediction to AUC $0.81$, a paired improvement of $0.08$ AUC (95\% CI $[0.03,0.13]$) that persists across classifiers and identity-subspace dimensions. A ground-truth simulation calibrated to the real embeddings further shows that identity removal helps when disease-related change is distinct from patient-specific variation but can be detrimental when the two overlap. These findings reveal a substantial, stable patient-linked component of longitudinal CT foundation-model representations, with implications both for privacy and for improving longitudinal disease biomarkers.