Non-Crossing Deep Quantile Regression for Distributional Survival Prediction

2026-08-17

AI Summary

This study addresses the limited flexibility and quantile crossing issues inherent in survival quantile regression by proposing the CNQ framework. Integrating Kolmogorov-Arnold Networks with Transformers, this method enforces quantile monotonicity structurally through non-crossing constraints and establishes multi-level joint finite-sample excess risk bounds. Extensive experiments across 27 simulation scenarios and six real-world cohorts demonstrate that CNQ achieves lower pinball loss and more accurate interval coverage compared to existing approaches. Furthermore, the framework effectively captures covariate heterogeneity, enabling precise distributional survival prediction and personalized risk assessment. These results highlight CNQ’s potential as a robust solution for complex survival analysis tasks requiring both theoretical guarantees and empirical performance.

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: https://github.com/BIG-S2/deepcnq

Problem

• Survival Analysis
• Quantile Regression
• Crossing Quantiles
• Right-Censored Data
• Distributional Prediction

Innovation

• Non-Crossing Quantile Regression
• Censored Data
• Kolmogorov-Arnold Networks
• Survival Analysis
• Distributional Prediction