Non-Crossing Deep Quantile Regression for Distributional Survival Prediction

Abstract:In survival analysis the way covariates act on the risk of an event often differs between early and late failure times, yet hazard- and mean-based summaries collapse this variation into a single number. Quantile-based modeling instead describes the full conditional distribution on the original time scale, but existing censored-data methods are either inflexible or produce logically inconsistent crossing quantile curves. We propose a Censored Non-crossing Quantile (CNQ) framework for right-censored data that jointly estimates several conditional survival quantiles and guarantees valid ordering by construction, with flexibility supplied by Kolmogorov-Arnold and Transformer backbones, and we establish a finite-sample excess-risk bound holding jointly across all fitted quantile levels. Across 27 simulation settings and six cohorts the framework attains lower pinball loss than quantile-, hazard- and tree-based competitors whenever the conditional distribution is asymmetric, with interval coverage closer to nominal on all six. In two clinical case studies (METABRIC, breast cancer; FLCHAIN, population mortality) it recovers covariate effects that vary across the survival distribution and would be hidden by a single hazard ratio, and yields coherent individualized quantile milestones. Code: this https URL

50 pages, 15 figures, 17 tables. Main text and supplementary material combined into a single document. Submitted to the Annals of Applied Statistics

Machine Learning (stat.ML); Machine Learning (cs.LG); Applications (stat.AP)

arXiv:2608.16864 [stat.ML]

(or arXiv:2608.16864v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2608.16864 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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