Hypothesis

Integrating patient‑specific similarity graphs into deep partially linear Cox networks that explicitly model hazard change‑points will uncover discrete biological phase transitions in aging trajectories, improving both discrimination and calibration relative to standard deep survival models.

Mechanistic Basis

Recent work shows that deep partially linear Cox models with change‑point detection achieve semiparametric efficiency and identify critical hazard shifts [2]; however, they treat each subject independently. Graph‑enhanced Cox models (Cox‑Sage) demonstrate that patient similarity networks can guide feature selection while preserving hazard interpretability [3]. We propose that the graph regularization term enforces smoothness of hazard functions across biologically similar individuals, allowing the change‑point detection component to shared transitions rather than noisy subject‑specific fluctuations. Mechanistically, aging is hypothesized to proceed through epochs where molecular networks (e.g., inflammasome activation, mitochondrial decline) undergo coordinated rewiring; these rewiring events manifest as sudden alterations in the hazard rate for multimorbidity or mortality. By coupling a graph Laplacian penalty on the latent hazard representation with a deep piecewise‑linear baseline, the model can align estimated hazard jumps with conserved network states, thereby providing a biologically grounded interpretation of each detected change‑point.

Testable Predictions

1. Improved calibration: On longitudinal aging cohorts (e.g., Framingham Heart Study, UK Biobank aging subset), the graph‑regularized change‑point Cox model will achieve calibration slopes closer to 1.0 (Hosmer‑Lemeshow p > 0.05) while maintaining a C‑index ≥0.80, surpassing DeepSurv and Cox‑Sage baselines which show calibration drift [4].
2. Consistent change‑point timing: Across individuals sharing high graph similarity (top 10 % of network edges), the distribution of detected hazard change‑points will exhibit significantly lower variance (Levene’s test p < 0.01) compared to random similarity groups.
3. Pathway enrichment: Features receiving high gradient‑based importance at each change‑point will be enriched for known aging pathways (e.g., senescence, IGF‑1 signaling) identified via GSEA (FDR < 0.05), linking statistical transitions to molecular processes.
4. Intervention simulation: In silico perturbation of graph edges (e.g., weakening connections between individuals with high inflammatory profiles) will shift the estimated change‑point distribution toward later ages, predicting a delay in hazard acceleration.

Experimental Design

• Data: Use multi‑omics longitudinal data from the UK Biobank (baseline + follow‑up visits up to 15 years) with transcriptomics, proteomics, and clinical covariates; restrict to participants ≥60 years at baseline (n≈8 000).
• Models: Compare (a) standard DeepSurv, (b) Cox‑Sage, (c) deep partially linear Cox with change‑points (no graph), (d) proposed graph‑regularized change‑point Cox.
• Evaluation: Compute time‑dependent C‑index, calibration curves (using risk deciles), and Brier score at 5‑ and 10‑year horizons. Perform change‑point consistency analysis via intraclass correlation coefficient (ICC) across graph clusters.
• Pathway analysis: Map top‑ranked features per change‑point to KEGG/Reactome pathways; run enrichment.
• Simulation: Generate synthetic aging trajectories with known phase shifts to verify recovery power under varying graph noise levels.

Potential Implications

If validated, this approach would translate survival analysis from static risk stratification to dynamic phase detection, enabling early identification of aging‑related tipping points. Clinically, it could inform timed interventions (e.g., senolytics, metabolic modulators) calibrated to an individual’s inferred biological epoch, addressing the current gap between high‑dimensional prediction and actionable insight in longevity research.