Non-Crossing Deep Quantile Regression for Distributional Survival Prediction
2026-08-17 • Machine Learning
Machine Learning
AI summaryⓘ
The authors point out that traditional survival analysis methods often summarize risk with a single number, which can miss how risks change over time. They introduce a new method called Censored Non-crossing Quantile (CNQ) for data where some observations are incomplete, which estimates several time points in the survival curve without contradictions. Their method uses advanced mathematical tools and performs better in simulations and real medical data, revealing patterns hidden by older methods. This helps understand how factors influence survival differently at various times.
Survival analysisRight-censored dataQuantile regressionHazard functionPinball lossKolmogorov-Arnold representationTransformer modelsConditional distributionExcess risk boundsSurvival quantiles
Authors
Shuai Huang, Zhe Qu, Zhaowei Hua, Guohao Shen, Rui Tang, Hongtu Zhu
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