Interpretable Hazard Models Reveal Strong Metastasis Dependence and Feature Interaction Effects in Predicting Cancer Patient Readmission Risk

Predicting hospital readmission in cancer patients-particularly those with metastatic disease-remains a significant clinical challenge. While metastasis is known to affect prognosis, its role in shaping the relationship between standard clinical features (e.g., lab tests) and readmission risk remains poorly understood. In this study, we leverage the MIMIC-IV database to stratify patients by metastatic burden, defined by the number of metastatic sites, and analyze survival dynamics using a two-step neural-symbolic distillation framework. First, assuming the proportional hazards structure, we train a neural network to learn both the baseline hazard h ₀ ( t ) and the log-partial hazard f ( x ), capturing complex, noisy survival patterns. We then distill the learned model into interpretable symbolic functions using Kolmogorov-Arnold Networks (KANs). For h ₀ ( t ), we observe metastasis-specific linear or quadratic trends, with significantly steeper early-time hazards in patients with three or more metastatic sites-highlighting the need for enhanced post-discharge monitoring. To simplify the symbolization of f ( x ), we introduce a prestructuring step using B -spline expansions with both univariate and interaction terms. This reduces symbolic complexity and reveals that interaction effects dominate, with larger coefficients than univariate terms in most subgroups. The resulting symbolic expressions for f ( x ) vary substantially across metastasis strata, indicating that the influence of lab-derived features on readmission is metastasis-dependent. Our framework offers interpretable, metastasis-stratified survival models and provides a foundation for deeper exploration of lab-metastasis interactions in personalized cancer care.