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Life sciences · Preprint
arXiv · August 17, 2026
Early or partial results. Treat as a signal, not a conclusion.
This preprint describes a novel deep quantile regression method (CNQ) for survival analysis that avoids crossing quantile curves and accommodates asymmetric conditional distributions. In simulations and two retrospective cohorts (METABRIC breast cancer, FLCHAIN mortality), the method shows better predictive accuracy than existing hazard- and quantile-based methods and recovers heterogeneous covariate effects across the survival distribution. The work is methodological and unreviewed; clinical utility and generalizability remain to be established.
Method development: simulation and retrospective cohort validation study. Simulated data and retrospective cohorts; specific cohort inclusion/exclusion criteria and sample sizes not stated.. Intervention: Censored Non-crossing Quantile (CNQ) regression framework with Kolmogorov-Arnold and Transformer backbones.. Compared with: Quantile-based, hazard-based, and tree-based survival prediction methods.. Not reported..
Attained lower pinball loss than quantile-, hazard- and tree-based competitors whenever the conditional distribution is asymmetric across 27 simulation settings Interval coverage closer to nominal on all six cohorts compared to competitors In METABRIC and FLCHAIN case studies, recovered covariate effects that vary across the survival distribution and would be hidden by a single hazard ratio
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If validated prospectively, this method could improve individualized survival prediction by characterizing how covariates affect different quantiles of the survival distribution rather than reducing to a single hazard ratio. However, current evidence is computational and retrospective; clinical utility and impact on treatment decisions remain unstudied.
A methodological study presenting a novel computational framework for survival analysis, validated on simulations and retrospective cohorts without prospective clinical trial data or peer review.
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If validated prospectively, this method could improve individualized survival prediction by characterizing how covariates affect different quantiles of the survival distribution rather than reducing to a single hazard ratio. However, current evidence is computational and retrospective; clinical utility and impact on treatment decisions remain unstudied.
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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: https://github.com/BIG-S2/deepcnq
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