Hypothesis

Integrating Weibull baseline hazards with neural Cox frameworks will improve prediction of mortality risk by explicitly modeling the two reported molecular waves of aging (45‑55 yr and 60‑65 yr) as distinct Weibull phases. This hybrid model tests whether hazard functions derived from omics‑driven neural networks exhibit piecewise Weibull shape parameters that correspond to these waves, and whether incorporating phase‑specific covariates enhances discrimination and calibration beyond standard DeepSurv or CoFormerSurv.

Mechanistic Rationale

Multi-omics clocks reveal non‑linear aging with peaks in transcriptomic, proteomic, and metabolomic alterations at mid‑life and later‑life intervals [5]. Engineering reliability theory treats failure processes as time‑varying, often modeled with Weibull distributions that accommodate changing hazard rates [8]. By treating each molecular wave as a Weibull phase, we allow the baseline hazard to shift shape (β) and scale (η) at transition points, reflecting altered underlying damage accumulation. The neural component then learns omics‑dependent modifiers of these Weibull parameters, capturing interactions that linear Cox or pure deep survival models miss.

Model Architecture

1. Input layer – normalized multi-omics features (transcriptomics, proteomics, metabolomics).
2. Shared MLP – extracts high‑level representation (as in DeepSurv) [1][2].
3. Phase‑specific heads – two parallel branches each outputting Weibull shape (β) and scale (η) parameters for Wave 1 and Wave 2.
4. Gating network – learns age‑dependent weights (softmax) that blend the two Weibull hazards, ensuring smooth transition near 55‑60 yr.
5. Risk score – weighted sum of phase hazards yields individual predicted hazard at any time t.

Loss function combines negative log‑likelihood of the Weibull‑Cox hybrid with L2 regularization.

Testable Predictions

• Discrimination – The Weibull‑phase model will achieve a concordance index ≥ 0.05 higher than DeepSurv and CoFormerSurv on independent longitudinal cohorts (e.g., UK BioBank, Framingham) after adjusting for covariates.
• Calibration – Calibration plots will show reduced systematic error across the 40‑80 yr age range, particularly around the 45‑55 yr and 60‑65 yr inflection points.
• Parameter Interpretation – Estimated β values will be significantly > 1 for Wave 2 (indicating accelerating hazard) and ≈ 1 for Wave 1 (constant hazard), matching engineering expectations of increasing failure rate with accumulated damage.
• Feature Importance – SHAP analysis will reveal that omics features driving Wave 1 are enriched for inflammation and metabolic pathways, whereas Wave 2 features emphasize proteostatic decline and mitochondrial dysfunction, providing mechanistic validation.
• Falsification – If the Weibull‑phase model does not outperform baseline neural Cox models or if estimated β parameters show no monotonic change across the hypothesized waves, the hypothesis is refuted.

Experimental Plan

1. Train Weibull‑phase neural Cox on baseline omics data from a training cohort (n ≈ 5 000) with time‑to‑event and censoring.
2. Validate on an external hold‑out set (n ≈ 2 000) reporting C‑index, integrated Brier score, and calibration slope.
3. Perform likelihood‑ratio test comparing nested models (standard DeepSurv vs. Weibull‑phase).
4. Use bootstrapping to assess stability of β and η estimates across resamples.
5. Conduct pathway enrichment on top SHAP features for each wave to confirm biological plausibility.

By explicitly linking engineering‑inspired temporal hazard shapes to multi‑omics aging waves, this hypothesis offers a concrete, falsifiable route to improve survival prediction while generating interpretable parameters that bridge machine learning reliability and mechanistic gerontology.