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 provides a powerful statistical framework for modeling time-to-event outcomes in the presence of censoring. However, selecting an appropriate estimator from the many specialized survival approaches often requires substantial methodological and domain expertise. We introduce SurvivalPFN, a prior-data fitted network that amortizes Bayesian inference for censored observations through in-context learning. SurvivalPFN is pretrained on a diverse family of synthetic, identifiable, and right-censored data-generating processes, enabling it to amortize survival analysis in a single forward pass during inference. As a result, the model adapts to the effective complexity of each dataset without task-specific training or hyperparameter tuning, avoids restrictive parametric assumptions, and produces calibrated survival distributions. In a large-scale benchmark spanning 61 datasets, 21 methods, and 5 evaluation metrics, SurvivalPFN achieves strong predictive performance and often improves upon established survival models. These results suggest that SurvivalPFN offers a principled and practical foundation model for survival analysis, with potential applications in high-impact domains such as healthcare, finance, and engineering (https://github.com/rgklab/SurvivalPFN).

Wemodel theeventofinterest asaspecial terminal state, andwe seek to estimate the survival distribution (i.e., the distribution of the hitting time for that terminal state) from anyother state.

This method effectively improves the model's marginal and conditional calibration,

Quantifying out-of-sample discrimination performance for time-to-event outcomes is a fundamental step for model evaluation and selection in the context of predictive modelling. The concordance index, or C-index, is a widely used metric for this purpose, particularly with the growing development of machine learning methods. Beyond differences between proposed C-index estimators (e.g. Harrell's, Uno's and Antolini's), we demonstrate the existence of a C-index multiverse among available R and python software, where seemingly equal implementations can yield different results. This can undermine reproducibility and complicate fair comparisons across models and studies. Key variation sources include tie handling and adjustment to censoring. Additionally, the absence of a standardised approach to summarise risk from survival distributions, result in another source of variation dependent on input types. We demonstrate the consequences of the C-index multiverse when quantifying predictive performance for several survival models (from Cox proportional hazards to recent deep learning approaches) on publicly available breast cancer data, and semi-synthetic examples. Our work emphasises the need for better reporting to improve transparency and reproducibility. This article aims to be a useful guideline, helping analysts when navigating the multiverse, providing unified documentation and highlighting potential pitfalls of existing software. All code is publicly available at: www.github.com/BBolosSierra/CindexMultiverse.

Survival prediction often involves estimating the time-to-event distribution from censored datasets. Previous approaches have focused on enhancing discrimination and marginal calibration. In this paper, we highlight the significance of conditional calibration for real-world applications -- especially its role in individual decision-making. We propose a method based on conformal prediction that uses the model's predicted individual survival probability at that instance's observed time. This method effectively improves the model's marginal and conditional calibration, without compromising discrimination. We provide asymptotic theoretical guarantees for both marginal and conditional calibration and test it extensively across 15 diverse real-world datasets, demonstrating the method's practical effectiveness and versatility in various settings.

Given an instance, a multi-event survival model predicts the time until that instance experiences each of several different events. These events are not mutually exclusive and there are often statistical dependencies between them. There are relatively few multi-event survival results, most focusing on producing a simple risk score, rather than the time-to-event itself. To overcome these issues, we introduce MENSA, a novel, deep learning approach for multi-event survival analysis that can jointly learn representations of the input covariates and the dependence structure between events. As a practical motivation for multi-event survival analysis, we consider the problem of predicting the time until a patient with amyotrophic lateral sclerosis (ALS) loses various physical functions, i.e., the ability to speak, swallow, write, or walk. When estimating when a patient is no longer able to swallow, our approach achieves an L1-Margin loss of 278.8 days, compared to 355.2 days when modeling each event separately. In addition, we also evaluate our approach in single-event and competing risk scenarios by modeling the censoring and event distributions as equal contributing factors in the optimization process, and show that our approach performs well across multiple benchmark datasets. The source code is available at: https://github.com/thecml/mensa

Identifying patient subgroups with different treatment responses is an important task to inform medical recommendations, guidelines, and the design of future clinical trials. Existing approaches for subgroup analysis primarily focus on Randomised Controlled Trials (RCTs), in which treatment assignment is randomised. Furthermore, the patient cohort of an RCT is often constrained by cost, and is not representative of the heterogeneity of patients likely to receive treatment in real-world clinical practice. Therefore, when applied to observational studies, such approaches suffer from significant statistical biases because of the non-randomisation of treatment. Our work introduces a novel, outcome-guided method for identifying treatment response subgroups in observational studies. Our approach assigns each patient to a subgroup associated with two time-to-event distributions: one under treatment and one under control regime. It hence positions itself in between individualised and average treatment effect estimation. The assumptions of our model result in a simple correction of the statistical bias from treatment non-randomisation through inverse propensity weighting. In experiments, our approach significantly outperforms the current state-of-the-art method for outcome-guided subgroup analysis in both randomised and observational treatment regimes.