Frailty-Based Patient Stratification in Hierarchical Survival Settings: From Mixture Models to Spectral Clustering

Alessandra Ragni and Luca Caldera

Politecnico di Milano

Thursday 26th March 2026

12:00:00

Saleri

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Real-world healthcare data often exhibit both substantial patient heterogeneity and hierarchical dependence induced by the healthcare institutions in which patients are treated. Properly accounting for these features in the identification of meaningful risk profiles can substantially improve decision-making in clinical studies involving time-to-event outcomes. In this talk, we present two methodological approaches for clustering patients in hierarchical survival data. Both methods aim to uncover latent subgroups of patients with similar risk patterns while accounting for institutional-level variability through shared frailty components. The first contribution introduces a cluster-weighted mixture model for right-censored survival data that jointly models the distribution of covariates and survival outcomes. The approach incorporates cluster-specific shared frailty terms to capture hospital-level variability, allowing a flexible characterization of heterogeneity in both patient profiles and survival responses. Parameter estimation is performed through EM-based algorithms that enable the identification of latent patient clusters and the evaluation of covariate effects within each subgroup. The second contribution proposes a likelihood-based framework that integrates parametric shared frailty survival models with adaptive spectral clustering. This method performs risk-driven patient stratification while simultaneously accounting for hierarchical dependence across healthcare institutions, leading to a unified estimation procedure for survival parameters and cluster structure. Both approaches are applied to administrative healthcare data concerning patients with heart failure hospitalized due to COVID-19 in the Lombardy region of Italy. The analyses reveal clinically interpretable patient subgroups and highlight substantial between-hospital variability in mortality risk. Together, these contributions demonstrate the importance of jointly modelling patient heterogeneity and hierarchical structures when developing data-driven strategies for risk stratification and clinical decision-making.