A Scalable Nonparametric Continuous-Time Survival Model through Numerical Quadrature

Survival analysis aims to estimate a time-to-event distribution from data with censored observations. Many existing methods either impose structural assumptions on the hazard function or discretize the time axis, which may limit flexibility and introduce approximation errors. We propose the Survival Diffusion Probabilistic Model (SDPM), a generative approach to continuous-time survival analysis. SDPM models the conditional distribution of the survival outcome, represented by the pair of observed time and censoring indicator, $\mathbb{P}(T,δ\mid \mathbf{x})$, using a denoising diffusion model. Under the assumption of conditionally independent censoring, conditional samples generated by the model can be transformed into survival function estimates using the Kaplan-Meier estimator. This formulation avoids parametric assumptions on the event-time distribution and does not require a discretization of the output time space. The model operates in a transformed target space, using standardized log-times and a continuous Gaussian-mixture representation of the censoring indicator. We evaluate SDPM on ten real survival datasets and compare it with five strong baselines, including tree-based, boosting-based, and neural survival models. Results show that SDPM achieves competitive predictive performance across C-index, integrated time-dependent AUC, and integrated Brier score. A study on synthetic Cox-Weibull data demonstrates that SDPM can recover the shape of an underlying continuous survival distribution more accurately than a strong nonparametric baseline when sufficiently many samples are generated. An ablation study confirms the importance of the proposed target-space transformations, which improve event-rate calibration, reduce invalid generated times, and provide consistent gains in predictive discrimination. Codes implementing the proposed model are publicly available.

Survival analysis aims to model how covariates and time jointly shape the time-to-event distribution under right censoring. Classical methods such as the Cox model and generalised additive models (GAMs) require interactions and time-varying effects to be manually specified, which is increasingly impractical on rich clinical datasets. We introduce KAPLAN-HR, a B-spline Kolmogorov-Arnold Network (KAN) for nonparametric estimation of the conditional hazard as a joint function of covariates and time. A single-layer KAPLAN-HR model recovers a GAM, while deeper architectures capture interactions and time-varying effects through composition. We establish a convergence rate for the nonparametric KAN hazard estimator that depends only on the smoothness of the underlying KAN representation and not on the covariate dimension, thereby mitigating the curse of dimensionality for KAN-representable targets. In evaluations over six clinical benchmark datasets, KAPLAN-HR matches or exceeds the predictive performance of established statistical and deep learning survival methods.

Survival analysis on tabular data is a well-studied problem. However, existing deep learning methods are often highly task-specific, which can limit the transfer of new approaches from other domains and introduce constraints that may affect performance. We propose TabSurv, an approach that adapts modern tabular architectures to survival analysis using either the Weibull distribution or non-parametric survival prediction. TabSurv optimizes SurvHL, a novel histogram loss function supporting censored data. In addition to a baseline feed-forward network, we implement deep ensembles of MLPs for survival analysis within TabSurv. In contrast to prior work, the ensemble components are trained in parallel, optimizing survival distribution parameters before averaging, which promotes diversity across ensemble component predictions. We perform a comprehensive empirical evaluation of different proposed architectures on 10 diverse real-world survival datasets. Our results show that TabSurv consistently outperforms on average established classical and deep learning baselines, such as RSF, DeepSurv, DeepHit, SurvTRACE. Notably, deep ensembles with Weibull parametrization instead of non-parametric models achieve the highest average rank by C-index. Overall, our study clarifies how modern tabular neural networks can be adapted and trained to tackle survival analysis problems, offering a strong and reliable approach. The TabSurv implementation is publicly available.