Survival Analysis

There remain theoretical gaps in deep neural network estimators for the nonparametric Cox proportional hazards model. In particular, it is unclear how gradient-based optimization error propagates to population risk under partial likelihood, how pointwise bias can be controlled to permit valid inference, and how ensemble-based uncertainty quantification behaves under realistic variance decay regimes. We develop an asymptotic distribution theory for deep Cox estimators that addresses these issues. First, we establish nonasymptotic oracle inequalities for general trained networks that link in-sample optimization error to population risk without requiring the exact empirical risk optimizer. We then construct a structured neural parameterization that achieves infinity-norm approximation rates compatible with the oracle bound, yielding control of the pointwise bias. Under these conditions and using the Hajek--Hoeffding projection, we prove pointwise and multivariate asymptotic normality for subsampled ensemble estimators. We derive a range of subsample sizes that balances bias correction with the requirement that the Hajek--Hoeffding projection remain dominant. This range accommodates decay conditions on the single-overlap covariance, which measures how strongly a single shared observation influences the estimator, and is weaker than those imposed in the subsampling literature. An infinitesimal jackknife representation provides analytic covariance estimation and valid Wald-type inference for relative risk contrasts such as log-hazard ratios. Finally, we illustrate the finite-sample implications of the theory through simulations and a real data application.

Optimizing survival outcomes, such as patient survival or customer retention, is a critical objective in data-driven decision-making. Off-Policy Evaluation~(OPE) provides a powerful framework for assessing such decision-making policies using logged data alone, without the need for costly or risky online experiments in high-stakes applications. However, typical estimators are not designed to handle right-censored survival outcomes, as they ignore unobserved survival times beyond the censoring time, leading to systematic underestimation of the true policy performance. To address this issue, we propose a novel framework for OPE and Off-Policy Learning~(OPL) tailored for survival outcomes under censoring. Specifically, we introduce IPCW-IPS and IPCW-DR, which employ the Inverse Probability of Censoring Weighting technique to explicitly deal with censoring bias. We theoretically establish that our estimators are unbiased and that IPCW-DR achieves double robustness, ensuring consistency if either the propensity score or the outcome model is correct. Furthermore, we extend this framework to constrained OPL to optimize policy value under budget constraints. We demonstrate the effectiveness of our proposed methods through simulation studies and illustrate their practical impacts using public real-world data for both evaluation and learning tasks.

Chronic diseases are long-lasting conditions that require lifelong medical attention. Using big EMR data, we have developed early disease risk prediction models for five common chronic diseases: diabetes, hypertension, CKD, COPD, and chronic ischemic heart disease. In this study, we present a novel approach for disease risk models by integrating survival analysis with classification techniques. Traditional models for predicting the risk of chronic diseases predominantly focus on either survival analysis or classification independently. In this paper, we show survival analysis methods can be re-engineered to enable them to do classification efficiently and effectively, thereby making them a comprehensive tool for developing disease risk surveillance models. The results of our experiments on real-world big EMR data show that the performance of survival models in terms of accuracy, F1 score, and AUROC is comparable to or better than that of prior state-of-the-art models like LightGBM and XGBoost. Lastly, the proposed survival models use a novel methodology to generate explanations, which have been clinically validated by a panel of three expert physicians.

While colorectal liver metastasis (CRLM) is potentially curable via hepatectomy, patient outcomes remain highly heterogeneous. Postoperative survival prediction is necessary to avoid non-beneficial surgeries and guide personalized therapy. In this study, we present an automated AI-based framework for postoperative CRLM survival prediction using pre- and post-contrast MRI. We performed a retrospective study of 227 CRLM patients who had gadoxetate-enhanced MRI prior to curative-intent hepatectomy between 2013 and 2020. We developed a survival prediction framework comprising an anatomy-aware segmentation pipeline followed by a radiomics pipeline. The segmentation pipeline learns liver, CRLMs, and spleen segmentation from partially-annotated data, leveraging promptable foundation models to generate pseudo-labels. To support this pipeline, we propose SAMONAI, a prompt propagation algorithm that extends Segment Anything Model to 3D point-based segmentation. Predicted pre- and post-contrast segmentations are then fed into our radiomics pipeline, which extracts per-tumor features and predicts survival using SurvAMINN, an autoencoder-based multiple instance neural network for time-to-event survival prediction. SurvAMINN jointly learns dimensionality reduction and survival prediction from right-censored data, emphasizing high-risk metastases. We compared our framework against established methods and biomarkers using univariate and multivariate Cox regression. Our segmentation pipeline achieves median Dice scores of 0.96 (liver) and 0.93 (spleen), driving a CRLM segmentation Dice score of 0.78 and a detection F1-score of 0.79. Accurate segmentation enables our radiomics pipeline to achieve a survival prediction C-index of 0.69. Our results show the potential of integrating segmentation algorithms with radiomics-based survival analysis to deliver accurate and automated CRLM outcome prediction.

Estimating heterogeneous treatment effects (HTEs) from right-censored survival data is critical in high-stakes applications such as precision medicine and individualized policy-making. Yet, the survival analysis setting poses unique challenges for HTE estimation due to censoring, unobserved counterfactuals, and complex identification assumptions. Despite recent advances, from Causal Survival Forests to survival meta-learners and outcome imputation approaches, evaluation practices remain fragmented and inconsistent. We introduce SurvHTE-Bench, the first comprehensive benchmark for HTE estimation with censored outcomes. The benchmark spans (i) a modular suite of synthetic datasets with known ground truth, systematically varying causal assumptions and survival dynamics, (ii) semi-synthetic datasets that pair real-world covariates with simulated treatments and outcomes, and (iii) real-world datasets from a twin study (with known ground truth) and from an HIV clinical trial. Across synthetic, semi-synthetic, and real-world settings, we provide the first rigorous comparison of survival HTE methods under diverse conditions and realistic assumption violations. SurvHTE-Bench establishes a foundation for fair, reproducible, and extensible evaluation of causal survival methods. The data and code of our benchmark are available at: https://github.com/Shahriarnz14/SurvHTE-Bench .

Precision medicine promises to transform health care by offering individualised treatments that dramatically improve clinical outcomes. A necessary prerequisite is to identify subgroups of patients who respond differently to different therapies. Current approaches are limited to static measures of treatment success, neglecting the repeated measures found in most clinical trials. Our approach combines the concept of partly conditional modelling with treatment effect estimation based on the Virtual Twins method. The resulting time-specific responses to treatment are characterised using survLIME, an extension of Local Interpretable Model-agnostic Explanations (LIME) to survival data. Performance was evaluated using synthetic data and applied to clinical trials examining the effectiveness of panitumumab to treat metastatic colorectal cancer. An area under the receiver operating characteristic curve (AUC) of 0.77 for identifying fixed responders was achieved in a 1000 patient simulation. When considering dynamic responders, partly conditional modelling increased the AUC from 0.597 to 0.685. Applying the approach to colorectal cancer trials found genetic mutations, sites of metastasis, and ethnicity as important factors for response to treatment. Our approach can accommodate a dynamic response to treatment while potentially providing better performance than existing methods in instances of a fixed response to treatment. When applied to clinical data we attain results consistent with the literature.

Temporal Web analytics increasingly relies on large-scale, longitudinal data to understand how users, content, and systems evolve over time. A rapidly growing frontier is the Temporal Web3: decentralized platforms whose behavior is recorded as immutable, time-stamped event streams. Despite the richness of this data, the field lacks shared, reproducible benchmarks that capture real-world temporal dynamics, specifically censoring and non-stationarity, across extended horizons. This absence slows methodological progress and limits the transfer of techniques between Web3 and broader Web domains. In this paper, we present the FinSurvival Challenge 2025 as a case study in benchmarking temporal Web3 intelligence. Using 21.8 million transaction records from the Aave v3 protocol, the challenge operationalized 16 survival prediction tasks to model user behavior transitions.We detail the benchmark design and the winning solutions, highlighting how domain-aware temporal feature construction significantly outperformed generic modeling approaches. Furthermore, we distill lessons for next-generation temporal benchmarks, arguing that Web3 systems provide a high-fidelity sandbox for studying temporal challenges, such as churn, risk, and evolution that are fundamental to the wider Web.

In many applications, it is important to identify subpopulations that survive longer or shorter than the rest of the population. In medicine, for example, it allows determining which patients benefit from treatment, and in predictive maintenance, which components are more likely to fail. Existing methods for discovering subgroups with exceptional survival characteristics rely on restrictive assumptions about the survival model (e.g. proportional hazards), require pre-discretized features, and, as they compare average statistics, tend to overlook individual heterogeneity. In this paper, we propose Sysurv, a non-parametric, fully differentiable method that discovers human-readable rules selecting subgroups with exceptional survival characteristics. Empirical evaluation on a wide range of datasets and settings, including a case study on cancer data, shows that Sysurv reveals insightful and actionable survival subgroups, outperforming the state of the art.

Clinical risk prediction models often underperform in real-world settings due to poor calibration, limited transportability, and subgroup disparities. These challenges are amplified in high-dimensional multimodal cancer datasets characterized by complex feature interactions and a p >> n structure. We present a fully reproducible multimodal machine learning framework for 5-year overall survival prediction in breast cancer, integrating clinical variables with high-dimensional transcriptomic and copy-number alteration (CNA) features from the METABRIC cohort. After variance- and sparsity-based filtering and dimensionality reduction, models were trained using stratified train/validation/test splits with validation-based hyperparameter tuning. Two survival approaches were compared: an elastic-net regularized Cox model (CoxNet) and a gradient-boosted survival tree model implemented using XGBoost. CoxNet provides embedded feature selection and stable estimation, whereas XGBoost captures nonlinear effects and higher-order interactions. Performance was assessed using time-dependent area under the ROC curve (AUC), average precision (AP), calibration curves, Brier score, and bootstrapped 95 percent confidence intervals. CoxNet achieved validation and test AUCs of 98.3 and 96.6, with AP values of 90.1 and 80.4. XGBoost achieved validation and test AUCs of 98.6 and 92.5, with AP values of 92.5 and 79.9. Fairness diagnostics showed stable discrimination across age groups, estrogen receptor status, molecular subtypes, and menopausal state. This work introduces a governance-oriented multimodal survival framework emphasizing calibration, fairness auditing, robustness, and reproducibility for high-dimensional clinical machine learning.

Dynamic predictions for longitudinal and time-to-event outcomes have become a versatile tool in precision medicine. Our work is motivated by the application of dynamic predictions in the decision-making process for primary biliary cholangitis patients. For these patients, serial biomarker measurements (e.g., bilirubin and alkaline phosphatase levels) are routinely collected to inform treating physicians of the risk of liver failure and guide clinical decision-making. Two popular statistical approaches to derive dynamic predictions are joint modelling and landmarking. However, recently, machine learning techniques have also been proposed. Each approach has its merits, and no single method exists to outperform all others. Consequently, obtaining the best possible survival estimates is challenging. Therefore, we extend the Super Learner framework to combine dynamic predictions from different models and procedures. Super Learner is an ensemble learning technique that allows users to combine different prediction algorithms to improve predictive accuracy and flexibility. It uses cross-validation and different objective functions of performance (e.g., squared loss) that suit specific applications to build the optimally weighted combination of predictions from a library of candidate algorithms. In our work, we pay special attention to appropriate objective functions for Super Learner to obtain the most optimal weighted combination of dynamic predictions. In our primary biliary cholangitis application, Super Learner presented unique benefits due to its ability to flexibly combine outputs from a diverse set of models with varying assumptions for equal or better predictive performance than any model fit separately.

Hazard and survival functions are natural, interpretable targets in time-to-event prediction, but their inherent non-additivity fundamentally limits standard additive explanation methods. We introduce Survival Functional Decomposition (SurvFD), a principled approach for analyzing feature interactions in machine learning survival models. By decomposing higher-order effects into time-dependent and time-independent components, SurvFD offers a previously unrecognized perspective on survival explanations, explicitly characterizing when and why additive explanations fail. Building on this theoretical decomposition, we propose SurvSHAP-IQ, which extends Shapley interactions to time-indexed functions, providing a practical estimator for higher-order, time-dependent interactions. Together, SurvFD and SurvSHAP-IQ establish an interaction- and time-aware interpretability approach for survival modeling, with broad applicability across time-to-event prediction tasks.

Flexible survival prediction does not by itself ensure valid inference for covariate effects or subject-specific survival probabilities. We develop FLEXI-Haz, a semiparametric deep neural network model for right-censored data that combines an interpretable linear component in the log-hazard with a flexible function of time and adjustment covariates. This formulation permits nonproportional nuisance effects while retaining interpretable regression parameters. Under regularity conditions, we establish nuisance convergence rates that are minimax optimal up to logarithmic factors over composite Holder classes, together with root-n-consistent, asymptotically normal, and semiparametrically efficient estimation of the regression parameter. For adjustment covariates with finite support, we derive the explicit influence function for cumulative hazard and construct a cross-fitted one-step estimator yielding asymptotically valid pointwise confidence intervals for subject-specific survival. Simulations demonstrate reduced bias and improved coverage relative to a proportional hazards comparator under time-varying nuisance effects. An analysis of the Rotterdam breast cancer data illustrates the consequences of flexible adjustment for inference on treatment associations.

Multimodal survival analysis aims to improve cancer prognosis using heterogeneous biomedical data, such as histopathology images and genomic profiles. A common strategy is to align representations across modalities so that shared signals can be captured. However, strong cross-modal alignment can also remove modality-specific evidence that is critical for survival prediction. In this paper, we revisit multimodal survival learning from a simple observation: effective models should first discover shared patterns across modalities, and then preserve modality-specific signals. This motivates a representation learning principle that we refer to as Together Then Apart. Based on this idea, we propose TTA, a framework that balances cross-modal alignment and representation distinctiveness. TTA first performs prototype-based alignment to capture shared survival-related structures between modalities. It then encourages modality-specific distinctiveness through an anchor-guided contrastive objective. To further account for modality imbalance and noisy correspondences, we model cross-modal interactions using unbalanced optimal transport. We evaluate the proposed approach on multiple TCGA cancer cohorts with paired histopathology and genomic data. TTA consistently improves survival prediction over recent multimodal survival models. Moreover, the learned prototype structures reveal interpretable cross-modal patterns associated with clinical outcomes.

We revisit Cox's proportional hazards model to improve variable selection in survival analysis. A square-root transformation of the partial likelihood renders the selection of the regularization parameter pivotal, free of the unknown baseline hazard and censoring mechanism. The resulting criterion borrows from information criteria such as BIC and from penalized regression methods such as the lasso, taking the best of both. On simulated and real data, our method substantially improves upon state-of-the-art approaches used daily in support recovery.

Dependent censoring occurs when the event time and censoring time are not conditionally independent given the observed covariates. This complicates survival model evaluation because widely used metrics, such as the Brier score, typically handle right-censoring using inverse probability of censoring weighting (IPCW). Unfortunately, IPCW is valid only when the estimated censoring distribution is independent of the event time. We propose a dependent Brier score based on an Archimedean copula and the Copula-Graphic estimator, and establish consistency and asymptotic normality of its margin-time estimator. To evaluate the metric, we introduce a semi-synthetic framework that creates realistic dependent censoring while preserving the original covariate structure and known event times. Across 12 datasets, the proposed metric reduces estimation error by 12-16% on average relative to IPCW. Source code is available at https://github.com/thecml/DependentEVAL.

In this study, we present a novel Survival Analysis algorithm designed to efficiently handle large-scale longitudinal data. Our approach draws inspiration from Reinforcement Learning principles, particularly the Deep Q-Network paradigm, extending Temporal Learning concepts to Survival Regression. A central argument in our method relies on temporal consistency, a recursive consistency condition between survival predictions made at consecutive states. Our framework introduces a delayed target network that decouples the generation of temporally consistent training targets from model updates, providing a more stable training signal while enabling mini-batch optimization and end-to-end training. Additionally, it supports arbitrarily complex architectures, enabling the modeling of intricate temporal dependencies. Through numerous experiments we provide empirical evidence demonstrating our framework's ability to exploit temporal consistency across datasets of varying sizes. Moreover, our algorithm outperforms benchmarks on datasets with long sequences, demonstrating its ability to capture long-term patterns. Finally, ablation studies show that the degree of target delay has a substantial effect on predictive performance and training variability. Across two distinct survival model families, delayed target updates consistently improve over the same-timescale baseline.