---
title: "Non-Crossing Deep Quantile Regression for Distributional Survival Prediction"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2608.16864v1"
permalink: "https://feed.astralor.com/items/itm_16f5ae6c2cb49015defaf1f4"
published: "2026-08-17T17:46:41.000Z"
score: 78
channel: "ai"
tags: ["CNQ Framework","Kolmogorov-Arnold Networks","Transformer","Quantile Regression","Survival Analysis"]
---

# Non-Crossing Deep Quantile Regression for Distributional Survival Prediction

## AI commentary

> This work connects non-crossing deep quantile regression with time-varying covariate effects in survival analysis, making it essential reading for medical AI prognosis teams. Rather than a single hazard ratio or survival curve, its individualized quantile milestones feel more actionable for clinical communication and can reveal dynamic risk patterns hidden by one HR.

## At a glance

Survival analysis often misses how covariates affect early versus late failure times because hazard- or mean-based summaries collapse variation into one number. This paper introduces Censored Non-crossing Quantile (CNQ), a framework that jointly estimates multiple conditional survival quantiles under right censoring while guaranteeing valid ordering by construction. Using Kolmogorov-Arnold and Transformer backbones, it also provides a finite-sample excess-risk bound across all quantile levels. Across 27 simulation settings and six cohorts, CNQ lowers pinball loss whenever the conditional distribution is asymmetric and achieves closer-to-nominal interval coverage. In METABRIC and FLCHAIN case studies, it recovers covariate effects that vary across the survival distribution and are hidden by a single hazard ratio.

## Key points

- CNQ jointly estimates multiple conditional survival quantiles with ordering guaranteed by construction.
- Uses Kolmogorov-Arnold and Transformer backbones, backed by a finite-sample excess-risk bound across all quantile levels.
- Across 27 simulations and six cohorts, CNQ beats quantile-, hazard-, and tree-based competitors under asymmetry, with coverage closer to nominal in all cohorts.
- METABRIC and FLCHAIN case studies recover covariate effects that vary across the survival distribution and would be hidden by a single hazard ratio.

## Full text

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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