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We introduce a new parametric approach for clustering multilevel survival data that accounts for the heterogeneity at baseline and random distributions of the explanatory variables. The proposed method aims to identify clusters of patients with different survival patterns and uncover the impact of the known hierarchy on survival within each cluster. The objective function is maximized using a stochastic EM algorithm tailored to right-censored lifetime data. The proposed methodology can be seen as a generalization of multilevel cluster-weighted modeling for time-to-event outcomes. Promising results are showcased on synthetic data.