Fusing Covariates and Censored Outcomes via Reliability-Weighted Diffusion

• Path-based forest similarity fuses covariates with censored outcomes. • Reliability-weighted diffusion recovers latent survival geometry. • Novel p-box test assesses separation under informative censoring. • Method outperforms deep baselines on benchmarks and synthetic data. • Contrastive rules offer interpretable summaries of survival strata. Survival clustering integrates two heterogeneous information sources: a partially observed, right-censored time-to-event signal and a fully observed covariate view. The goal is to identify subgroups that are both structurally coherent and prognostically distinct. However, standard methods often fail to balance these conflicting objectives, favoring partitions with overlapping survival curves or isolating groups with poor covariate consistency. We introduce a fusion framework based on a survival-tree path similarity . Subject affinity is derived from shared decision paths across log-rank–split ensembles, combined with out-of-bag restriction and bootstrap multiplicity. This similarity drives a pipeline combining diffusion-based embedding and clustering, yielding interpretable low-dimensional visualisations. To assess separation without relying directly on Kaplan–Meier-based summaries, which may be misleading under informative censoring, we use a discrepancy based on empirical p-boxes (probability boxes), together with a conditional permutation calibration for a fixed partition. We validate the approach on (i) synthetic datasets with known ground truth, (ii) established survival-clustering benchmarks, and (iii) a real-world cohort of substance-use treatment admissions from Asturias (Spain). Results show that path-based RSF similarities combined with manifold learning attain competitive or improved survival separation while preserving geometric coherence, especially under informative censoring.