Survival analysis is central to clinical decision-making, yet reliable time-to-event models require large, diverse cohorts that are rarely available at a single institution, while privacy regulations restrict the centralization of patient data. Federated learning (FL) offers a privacy-preserving alternative by training shared models without exchanging raw data, but its effectiveness for survival modeling under realistic, heterogeneous conditions remains insufficiently understood. This paper presents a systematic, multi-model evaluation of federated survival analysis on a cross-institutional breast cancer cohort with naturally heterogeneous distributed clients. Three representative survival models, the Cox Proportional Hazards model, DeepSurv, and Random Survival Forest (RSF), are compared across centralized, local, and federated training, and three federated optimization strategies (FedAvg, FedProx, and FedAdam) are assessed for the gradient-based models. Results show that FL consistently outperforms local training and approaches, and occasionally exceeds, centralized performance, while RSF offers the best overall balance of discrimination, calibration, and robustness across heterogeneous clients. We further find that performance depends on the diversity of client distributions, and that FedAvg and FedProx are stronger and more stable than FedAdam. Based on these findings, we derive practical, decision-oriented guidelines mapping data, privacy, interpretability, and resource constraints to recommended model and training-paradigm choices for federated survival modeling in healthcare.

Classical statistical learning theory predicts a U-shaped relationship between test loss and model capacity, driven by the bias-variance trade-off. Recent advances in modern machine learning have revealed a more complex pattern, \textit{double-descent}, in which test loss, after peaking near the interpolation threshold, decreases again as model capacity continues to grow. While this behavior has been extensively analyzed in regression and classification, its manifestation in survival analysis remains unexplored. This study investigates overparametrization in four representative survival models: DeepSurv, PC-Hazard, Nnet-Survival, and N-MTLR. We rigorously define \textit{interpolation} and \textit{finite-norm interpolation}, two key characteristics of loss-based models to understand \textit{double-descent}. We then show the existence (or absence) of \textit{(finite-norm) interpolation} of all four models. Our findings clarify how likelihood-based losses and model implementation jointly determine the feasibility of \textit{interpolation} and show that overparametrization should not be regarded as benign for survival models. All theoretical results are supported by numerical experiments that highlight the distinct generalization behaviors of survival models.

This study quantifies the association between non-adherence to antipsychotic medications and adverse outcomes in individuals with schizophrenia. We frame the problem using survival analysis, focusing on the time to the earliest of several adverse events (early death, involuntary hospitalization, jail booking). We extend standard causal inference methods (T-learner, S-learner, nearest neighbor matching) to utilize various survival models to estimate individual and average treatment effects, where treatment corresponds to medication non-adherence. Analyses are repeated using different amounts of longitudinal information (3, 6, 9, and 12 months). Using data from Allegheny County in western Pennsylvania, we find strong evidence that non-adherence advances adverse outcomes by approximately 1 to 4 months. Ablation studies confirm that county-provided risk scores adjust for key confounders, as their removal amplifies the estimated effects. Subgroup analyses by medication formulation (injectable vs. oral) and medication type consistently show that non-adherence is associated with earlier adverse events. These findings highlight the clinical importance of adherence in delaying psychiatric crises and show that integrating survival analysis with causal inference tools can yield policy-relevant insights. We caution that although we apply causal inference, we only make associative claims and discuss assumptions needed for causal interpretation.

Survival analysis is widely deployed in a diverse set of fields, including healthcare, business, ecology, etc. The Cox Proportional Hazard (CoxPH) model is a semi-parametric model often encountered in the literature. Despite its popularity, wide deployment, and numerous variants, scaling CoxPH to large datasets and deep architectures poses a challenge, especially in the high-dimensional regime. We identify a fundamental connection between rank regression and the CoxPH model: this allows us to adapt and extend the so-called spectral method for rank regression to survival analysis. Our approach is versatile, naturally generalizing to several CoxPH variants, including deep models. We empirically verify our method's scalability on multiple real-world high-dimensional datasets; our method outperforms legacy methods w.r.t. predictive performance and efficiency.

Predicting the risk of clinical progression from cognitively normal (CN) status to mild cognitive impairment (MCI) or Alzheimer's disease (AD) is critical for early intervention in Alzheimer's disease (AD). Traditional survival models often fail to capture complex longitudinal biomarker patterns associated with disease progression. We propose an ensemble survival analysis framework integrating multiple survival models to improve early prediction of clinical progression in initially cognitively normal individuals. We analyzed longitudinal biomarker data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) cohort, including 721 participants, limiting analysis to up to three visits (baseline, 6-month follow-up, 12-month follow-up). Of these, 142 (19.7%) experienced clinical progression to MCI or AD. Our approach combined penalized Cox regression (LASSO, Elastic Net) with advanced survival models (Random Survival Forest, DeepSurv, XGBoost). Model predictions were aggregated using ensemble averaging and Bayesian Model Averaging (BMA). Predictive performance was assessed using Harrell's concordance index (C-index) and time-dependent area under the curve (AUC). The ensemble model achieved a peak C-index of 0.907 and an integrated time-dependent AUC of 0.904, outperforming baseline-only models (C-index 0.608). One follow-up visit after baseline significantly improved prediction accuracy (48.1% C-index, 48.2% AUC gains), while adding a second follow-up provided only marginal gains (2.1% C-index, 2.7% AUC). Our ensemble survival framework effectively integrates diverse survival models and aggregation techniques to enhance early prediction of preclinical AD progression. These findings highlight the importance of leveraging longitudinal biomarker data, particularly one follow-up visit, for accurate risk stratification and personalized intervention strategies.

Survival analysis is a branch of statistics used for modeling the time until a specific event occurs and is widely used in medicine, engineering, finance, and many other fields. When choosing survival models, there is typically a trade-off between performance and interpretability, where the highest performance is achieved by black-box models based on deep learning. This is a major problem in fields such as medicine where practitioners are reluctant to blindly trust black-box models to make important patient decisions. Kolmogorov-Arnold Networks (KANs) were recently proposed as an interpretable and accurate alternative to multi-layer perceptrons (MLPs). We introduce CoxKAN, a Cox proportional hazards Kolmogorov-Arnold Network for interpretable, high-performance survival analysis. We evaluate the proposed CoxKAN on 4 synthetic datasets and 9 real medical datasets. The synthetic experiments demonstrate that CoxKAN accurately recovers interpretable symbolic formulae for the hazard function, and effectively performs automatic feature selection. Evaluation on the 9 real datasets show that CoxKAN consistently outperforms the Cox proportional hazards model and achieves performance that is superior or comparable to that of tuned MLPs. Furthermore, we find that CoxKAN identifies complex interactions between predictor variables that would be extremely difficult to recognise using existing survival methods, and automatically finds symbolic formulae which uncover the precise effect of important biomarkers on patient risk.

We propose a general approach for encouraging fairness in survival analysis models based on minimizing a worst-case error across all subpopulations that occur with at least a user-specified probability. This approach can be used to convert many existing survival analysis models into ones that simultaneously encourage fairness, without requiring the user to specify which attributes or features to treat as sensitive in the training loss function. From a technical standpoint, our approach applies recent developments of distributionally robust optimization (DRO) to survival analysis. The complication is that existing DRO theory uses a training loss function that decomposes across contributions of individual data points, i.e., any term that shows up in the loss function depends only on a single training point. This decomposition does not hold for commonly used survival loss functions, including for the Cox proportional hazards model, its deep neural network variants, and many other recently developed models that use loss functions involving ranking or similarity score calculations. We address this technical hurdle using a sample splitting strategy. We demonstrate our sample splitting DRO approach by using it to create fair versions of a diverse set of existing survival analysis models including the Cox model (and its deep variant DeepSurv), the discrete-time model DeepHit, and the neural ODE model SODEN. We also establish a finite-sample theoretical guarantee to show what our sample splitting DRO loss converges to. For the Cox model, we further derive an exact DRO approach that does not use sample splitting. For all the models that we convert into DRO variants, we show that the DRO variants often score better on recently established fairness metrics (without incurring a significant drop in accuracy) compared to existing survival analysis fairness regularization techniques.

Survival analysis is essential for studying time-to-event outcomes and providing a dynamic understanding of the probability of an event occurring over time. Various survival analysis techniques, from traditional statistical models to state-of-the-art machine learning algorithms, support healthcare intervention and policy decisions. However, there remains ongoing discussion about their comparative performance. We conducted a comparative study of several survival analysis methods, including Cox proportional hazards (CoxPH), stepwise CoxPH, elastic net penalized Cox model, Random Survival Forests (RSF), Gradient Boosting machine (GBM) learning, AutoScore-Survival, DeepSurv, time-dependent Cox model based on neural network (CoxTime), and DeepHit survival neural network. We applied the concordance index (C-index) for model goodness-of-fit, and integral Brier scores (IBS) for calibration, and considered the model interpretability. As a case study, we performed a retrospective analysis of patients admitted through the emergency department of a tertiary hospital from 2017 to 2019, predicting 90-day all-cause mortality based on patient demographics, clinicopathological features, and historical data. The results of the C-index indicate that deep learning achieved comparable performance, with DeepSurv producing the best discrimination (DeepSurv: 0.893; CoxTime: 0.892; DeepHit: 0.891). The calibration of DeepSurv (IBS: 0.041) performed the best, followed by RSF (IBS: 0.042) and GBM (IBS: 0.0421), all using the full variables. Moreover, AutoScore-Survival, using a minimal variable subset, is easy to interpret, and can achieve good discrimination and calibration (C-index: 0.867; IBS: 0.044). While all models were satisfactory, DeepSurv exhibited the best discrimination and calibration. In addition, AutoScore-Survival offers a more parsimonious model and excellent interpretability.

Survival analysis is a valuable tool for estimating the time until specific events, such as death or cancer recurrence, based on baseline observations. This is particularly useful in healthcare to prognostically predict clinically important events based on patient data. However, existing approaches often have limitations; some focus only on ranking patients by survivability, neglecting to estimate the actual event time, while others treat the problem as a classification task, ignoring the inherent time-ordered structure of the events. Furthermore, the effective utilization of censored samples - training data points where the exact event time is unknown - is essential for improving the predictive accuracy of the model. In this paper, we introduce CenTime, a novel approach to survival analysis that directly estimates the time to event. Our method features an innovative event-conditional censoring mechanism that performs robustly even when uncensored data is scarce. We demonstrate that our approach forms a consistent estimator for the event model parameters, even in the absence of uncensored data. Furthermore, CenTime is easily integrated with deep learning models with no restrictions on batch size or the number of uncensored samples. We compare our approach with standard survival analysis methods, including the Cox proportional-hazard model and DeepHit. Our results indicate that CenTime offers state-of-the-art performance in predicting time-to-death while maintaining comparable ranking performance. Our implementation is publicly available at https://github.com/ahmedhshahin/CenTime.

We propose a general approach for training survival analysis models that minimizes a worst-case error across all subpopulations that are large enough (occurring with at least a user-specified minimum probability). This approach uses a training loss function that does not know any demographic information to treat as sensitive. Despite this, we demonstrate that our proposed approach often scores better on recently established fairness metrics (without a significant drop in prediction accuracy) compared to various baselines, including ones which directly use sensitive demographic information in their training loss. Our code is available at: https://github.com/discovershu/DRO_COX