Hypothesis

We propose a Hierarchical Temporal Multi-Omics Neural Cox (HTMON-Cox) architecture that integrates longitudinal transcriptomic, proteomic, and metabolomic measurements via a shared transformer encoder, couples this to a Cox proportional hazards layer through a time‑varying hazard head, and imposes a viscoelastic‑inspired regularization that forces the learned hazard contributions to relax across age strata in a manner analogous to polymeric aging. This regularization encodes age‑dependent hazard heterogeneity directly into the network structure, eliminating the need for post‑hoc subgroup analysis and improving long‑term calibration for 5‑year mortality predictions in individuals aged 85+.

Mechanistic Rationale

Recent work shows that neural Cox extensions capture non‑linear risk patterns 1 and transformer‑based biological age models separate mortality risk groups 2. However, mortality hazard in extreme aging is not static; biomarker trajectories exhibit delayed, history‑dependent effects reminiscent of stress‑relaxation in viscoelastic materials, where the current strain (hazard) depends on the integral of past strain weighted by a relaxation spectrum. By embedding a Prony‑series‑style kernel as a learnable regularization term on the transformer’s output, we constrain each omics‑derived hazard component to decay with stratum‑specific time constants (short‑term for inflammatory proteomics, long‑term for mitochondrial metabolomics). This mirrors adaptive architecture strategies from materials science that tailor internal structure to heterogeneous loading conditions 4.

Testable Predictions

1. Discrimination: HTMON-Cox will achieve a C‑index ≥0.88 on held‑out test sets of longitudinal multi‑omics aging cohorts, surpassing DeepSurv (0.83‑0.87) and transformer biological age models.
2. Calibration: The model’s calibration slope for 5‑year mortality will be statistically indistinguishable from 1.0 (p>0.05) in the 85‑89 and 95‑99 age strata, whereas baseline models will show significant mis‑calibration (slope <0.8).
3. Interpretability: SHAP values will reveal that hazard contributions from early‑life transcriptomic spikes decay faster than those from late‑life metabolomic shifts, consistent with the learned relaxation spectra.
4. Falsifiability: If HTMON‑Cox fails to improve calibration (slope remains <0.8) despite equal or better discrimination, the viscoelastic regularization hypothesis is refuted.

Experimental Design

• Cohort: Use the UK Biobank aging sub‑set with ≥3 longitudinal visits and matched transcriptome, proteome, and metabolome profiles (n≈2,500).
• Preprocessing: Apply MICE imputation for missing omics 3 and log‑transform.
• Model: Transformer encoder (4 layers, 8 heads) → shared representation → hazard head (Cox partial likelihood) + viscoelastic regularization term (learnable Prony series with 3 exponentials, constrained to be positive). Train with negative log‑partial likelihood plus L2 weight decay.
• Baselines: DeepSurv, DySurv with time‑varying covariates, and a static multi‑omics Cox net.
• Evaluation: Time‑dependent C‑index, integrated Brier score, calibration plots at 1, 3, 5 years; statistical comparison via bootstrap (1,000 resamples).
• Ablation: Remove viscoelastic term, replace with age‑stratum covariates, and test impact on calibration.

Potential Pitfalls

• Over‑regularization may suppress true non‑linear hazard signals; mitigated by cross‑validating the number of Prony terms.
• Sparse long‑term metabolomic sampling could bias relaxation spectra; addressed by incorporating dropout‑aware loss weighting.
• Computational cost of transformer on high‑dimensional omics; alleviated by feature‑wise variational autoencoder pre‑training.

If HTMON‑Cox demonstrates superior long‑term calibration while preserving discrimination, it will establish a mechanistic bridge between materials‑inspired adaptive architectures and survival modeling, offering a clinically actionable tool for risk stratification in the oldest old.