Adaptive Spectral Clustering in Shared-Frailty Survival Models for Risk-Based Patients Stratification

Stratifying patients according to their risk of experiencing an event of interest, while accounting for institutional effects induced by hierarchical data structures, contributes to improving clinical decision-making in real-world studies involving time-to-event outcomes. In this work, we analyze administrative healthcare data from the Enhance-Heart study that include heart failure patients hospitalized for COVID-19 in the Lombardy Region (Italy) over a period of approximately one and a half years, to identify patient subgroups with similar event risk while accounting for hospital-level dependence. To do so, we propose a likelihood-based survival modeling framework that integrates a parametric shared frailty model with a spectral clustering approach, enabling joint estimation of risk-driven patient clusters and survival parameters within a unified penalized optimization framework. Our results uncover clinically interpretable patient subgroups and not negligible between-hospital variability in mortality risk, demonstrating the value of jointly modeling patient stratification and hierarchical dependence in time-to-event data.