Survival analysis is a fundamental tool for modeling time-to-event data in healthcare, engineering, and finance, where censored observations pose significant challenges. While traditional methods like the Beran estimator offer nonparametric solutions, they often struggle with the complex data structures and heavy censoring. This paper introduces three novel survival models, iSurvM (the imprecise Survival model based on Mean likelihood functions), iSurvQ (the imprecise Survival model based on the Quantiles of likelihood functions), and iSurvJ (the imprecise Survival model based on the Joint learning), that combine imprecise probability theory with attention mechanisms to handle censored data without parametric assumptions. The first idea behind the models is to represent censored observations by interval-valued probability distributions for each instance over time intervals between events moments. The second idea is to employ the kernel-based Nadaraya-Watson regression with trainable attention weights for computing the imprecise probability distribution over time intervals for the entire dataset. The third idea is to consider three decision strategies for training, which correspond to the proposed three models. Experiments on synthetic and real datasets demonstrate that the proposed models, especially iSurvJ, consistently outperform the Beran estimator from the accuracy and computational complexity points of view. Codes implementing the proposed models are publicly available.
In Computational Pathology (CPath), the introduction of Vision-Language Models (VLMs) has opened new avenues for research, focusing primarily on aligning image-text pairs at a single magnification level. However, this approach might not be sufficient for tasks like cancer subtype classification, tissue phenotyping, and survival analysis due to the limited level of detail that a single-resolution image can provide. Addressing this, we propose a novel multi-resolution paradigm leveraging Whole Slide Images (WSIs) to extract histology patches at multiple resolutions and generate corresponding textual descriptions through advanced CPath VLM. We introduce visual-textual alignment at multiple resolutions as well as cross-resolution alignment to establish more effective text-guided visual representations. Cross-resolution alignment using a multimodal encoder enhances the model's ability to capture context from multiple resolutions in histology images. Our model aims to capture a broader range of information, supported by novel loss functions, enriches feature representation, improves discriminative ability, and enhances generalization across different resolutions. Pre-trained on a comprehensive TCGA dataset with 34 million image-language pairs at various resolutions, our fine-tuned model outperforms state-of-the-art (SOTA) counterparts across multiple datasets and tasks, demonstrating its effectiveness in CPath. The code is available on GitHub at: https://github.com/BasitAlawode/MR-PLIP
Survival analysis, which estimates the probability of event occurrence over time from censored data, is fundamental in numerous real-world applications, particularly in high-stakes domains such as healthcare and risk assessment. Despite advances in numerous survival models, quantifying the uncertainty of predictions from these models remains underexplored and challenging. The lack of reliable uncertainty quantification limits the interpretability and trustworthiness of survival models, hindering their adoption in clinical decision-making and other sensitive applications. To bridge this gap, in this work, we introduce SurvUnc, a novel meta-model based framework for post-hoc uncertainty quantification for survival models. SurvUnc introduces an anchor-based learning strategy that integrates concordance knowledge into meta-model optimization, leveraging pairwise ranking performance to estimate uncertainty effectively. Notably, our framework is model-agnostic, ensuring compatibility with any survival model without requiring modifications to its architecture or access to its internal parameters. Especially, we design a comprehensive evaluation pipeline tailored to this critical yet overlooked problem. Through extensive experiments on four publicly available benchmarking datasets and five representative survival models, we demonstrate the superiority of SurvUnc across multiple evaluation scenarios, including selective prediction, misprediction detection, and out-of-domain detection. Our results highlight the effectiveness of SurvUnc in enhancing model interpretability and reliability, paving the way for more trustworthy survival predictions in real-world applications.
Multimodal pathology-genomic analysis has become increasingly prominent in cancer survival prediction. However, existing studies mainly utilize multi-instance learning to aggregate patch-level features, neglecting the information loss of contextual and hierarchical details within pathology images. Furthermore, the disparity in data granularity and dimensionality between pathology and genomics leads to a significant modality imbalance. The high spatial resolution inherent in pathology data renders it a dominant role while overshadowing genomics in multimodal integration. In this paper, we propose a multimodal survival prediction framework that incorporates hypergraph learning to effectively capture both contextual and hierarchical details from pathology images. Moreover, it employs a modality rebalance mechanism and an interactive alignment fusion strategy to dynamically reweight the contributions of the two modalities, thereby mitigating the pathology-genomics imbalance. Quantitative and qualitative experiments are conducted on five TCGA datasets, demonstrating that our model outperforms advanced methods by over 3.4\% in C-Index performance.
Survival analysis often relies on Cox models, assuming both linearity and proportional hazards (PH). This study evaluates machine and deep learning methods that relax these constraints, comparing their performance with penalized Cox models on a benchmark of three synthetic and three real datasets. In total, eight different models were tested, including six non-linear models of which four were also non-PH. Although Cox regression often yielded satisfactory performance, we showed the conditions under which machine and deep learning models can perform better. Indeed, the performance of these methods has often been underestimated due to the improper use of Harrell's concordance index (C-index) instead of more appropriate scores such as Antolini's concordance index, which generalizes C-index in cases where the PH assumption does not hold. In addition, since occasionally high C-index models happen to be badly calibrated, combining Antolini's C-index with Brier's score is useful to assess the overall performance of a survival method. Results on our benchmark data showed that survival prediction should be approached by testing different methods to select the most appropriate one according to sample size, non-linearity and non-PH conditions. To allow an easy reproducibility of these tests on our benchmark data, code and documentation are freely available at https://github.com/compbiomed-unito/survhive.
Survival Regression (SuR) is a key technique for modeling time to event in important applications such as clinical trials and semiconductor manufacturing. Currently, SuR algorithms belong to one of three classes: non-linear black-box -- allowing adaptability to many datasets but offering limited interpretability (e.g., tree ensembles); linear glass-box -- being easier to interpret but limited to modeling only linear interactions (e.g., Cox proportional hazards); and non-linear glass-box -- allowing adaptability and interpretability, but empirically found to have several limitations (e.g., explainable boosting machines, survival trees). In this work, we investigate whether Symbolic Regression (SR), i.e., the automated search of mathematical expressions from data, can lead to non-linear glass-box survival models that are interpretable and accurate. We propose an evolutionary, multi-objective, and multi-expression implementation of SR adapted to SuR. Our empirical results on five real-world datasets show that SR consistently outperforms traditional glass-box methods for SuR in terms of accuracy per number of dimensions in the model, while exhibiting comparable accuracy with black-box methods. Furthermore, we offer qualitative examples to assess the interpretability potential of SR models for SuR. Code at: https://github.com/lurovi/SurvivalMultiTree-pyNSGP.
In this paper, we study the offline sequential feature-based pricing and inventory control problem where the current demand depends on the past demand levels and any demand exceeding the available inventory is lost. Our goal is to leverage the offline dataset, consisting of past prices, ordering quantities, inventory levels, covariates, and censored sales levels, to estimate the optimal pricing and inventory control policy that maximizes long-term profit. While the underlying dynamic without censoring can be modeled by Markov decision process (MDP), the primary obstacle arises from the observed process where demand censoring is present, resulting in missing profit information, the failure of the Markov property, and a non-stationary optimal policy. To overcome these challenges, we first approximate the optimal policy by solving a high-order MDP characterized by the number of consecutive censoring instances, which ultimately boils down to solving a specialized Bellman equation tailored for this problem. Inspired by offline reinforcement learning and survival analysis, we propose two novel data-driven algorithms to solving these Bellman equations and, thus, estimate the optimal policy. Furthermore, we establish finite sample regret bounds to validate the effectiveness of these algorithms. Finally, we conduct numerical experiments to demonstrate the efficacy of our algorithms in estimating the optimal policy. To the best of our knowledge, this is the first data-driven approach to learning optimal pricing and inventory control policies in a sequential decision-making environment characterized by censored and dependent demand. The implementations of the proposed algorithms are available at https://github.com/gundemkorel/Inventory_Pricing_Control
Cancer remains a leading global health challenge and a major cause of mortality. This study leverages machine learning (ML) to predict the survivability of cancer patients with metastatic patterns using the comprehensive MSK-MET dataset, which includes genomic and clinical data from 25,775 patients across 27 cancer types. We evaluated five ML models-XGBoost, Na\"ive Bayes, Decision Tree, Logistic Regression, and Random Fores using hyperparameter tuning and grid search. XGBoost emerged as the best performer with an area under the curve (AUC) of 0.82. To enhance model interpretability, SHapley Additive exPlanations (SHAP) were applied, revealing key predictors such as metastatic site count, tumor mutation burden, fraction of genome altered, and organ-specific metastases. Further survival analysis using Kaplan-Meier curves, Cox Proportional Hazards models, and XGBoost Survival Analysis identified significant predictors of patient outcomes, offering actionable insights for clinicians. These findings could aid in personalized prognosis and treatment planning, ultimately improving patient care.
The Cox proportional hazards (CPH) model has been widely applied in survival analysis to estimate relative risks across different subjects given multiple covariates. Traditional CPH models rely on a linear combination of covariates weighted with coefficients as the log-risk function, which imposes a strong and restrictive assumption, limiting generalization. Recent deep learning methods enable non-linear log-risk functions. However, they often lack interpretability due to the end-to-end training mechanisms. The implementation of Kolmogorov-Arnold Networks (KAN) offers new possibilities for extending the CPH model with fully transparent and symbolic non-linear log-risk functions. In this paper, we introduce Generalized Cox Proportional Hazards (GCPH) model, a novel method for survival analysis that leverages KAN to enable a non-linear mapping from covariates to survival outcomes in a fully symbolic manner. GCPH maintains the interpretability of traditional CPH models while allowing for the estimation of non-linear log-risk functions. Experiments conducted on both synthetic data and various public benchmarks demonstrate that GCPH achieves competitive performance in terms of prediction accuracy and exhibits superior interpretability compared to current state-of-the-art methods.
The integration of pathologic images and genomic data for survival analysis has gained increasing attention with advances in multimodal learning. However, current methods often ignore biological characteristics, such as heterogeneity and sparsity, both within and across modalities, ultimately limiting their adaptability to clinical practice. To address these challenges, we propose AdaMHF: Adaptive Multimodal Hierarchical Fusion, a framework designed for efficient, comprehensive, and tailored feature extraction and fusion. AdaMHF is specifically adapted to the uniqueness of medical data, enabling accurate predictions with minimal resource consumption, even under challenging scenarios with missing modalities. Initially, AdaMHF employs an experts expansion and residual structure to activate specialized experts for extracting heterogeneous and sparse features. Extracted tokens undergo refinement via selection and aggregation, reducing the weight of non-dominant features while preserving comprehensive information. Subsequently, the encoded features are hierarchically fused, allowing multi-grained interactions across modalities to be captured. Furthermore, we introduce a survival prediction benchmark designed to resolve scenarios with missing modalities, mirroring real-world clinical conditions. Extensive experiments on TCGA datasets demonstrate that AdaMHF surpasses current state-of-the-art (SOTA) methods, showcasing exceptional performance in both complete and incomplete modality settings.
Multimodal learning combining pathology images and genomic sequences enhances cancer survival analysis but faces clinical implementation barriers due to limited access to genomic sequencing in under-resourced regions. To enable survival prediction using only whole-slide images (WSI), we propose the Visual-Genomic Answering-Guided Transformer (VGAT), a framework integrating Visual Question Answering (VQA) techniques for genomic modality reconstruction. By adapting VQA's text feature extraction approach, we derive stable genomic representations that circumvent dimensionality challenges in raw genomic data. Simultaneously, a cluster-based visual prompt module selectively enhances discriminative WSI patches, addressing noise from unfiltered image regions. Evaluated across five TCGA datasets, VGAT outperforms existing WSI-only methods, demonstrating the viability of genomic-informed inference without sequencing. This approach bridges multimodal research and clinical feasibility in resource-constrained settings. The code link is https://github.com/CZZZZZZZZZZZZZZZZZ/VGAT.
There are many approaches for training decision trees. This work introduces a novel gradient-based method for constructing decision trees that optimize arbitrary differentiable loss functions, overcoming the limitations of heuristic splitting rules. Unlike traditional approaches that rely on heuristic splitting rules, the proposed method refines predictions using the first and second derivatives of the loss function, enabling the optimization of complex tasks such as classification, regression, and survival analysis. We demonstrate the method's applicability to classification, regression, and survival analysis tasks, including those with censored data. Numerical experiments on both real and synthetic datasets compare the proposed method with traditional decision tree algorithms, such as CART, Extremely Randomized Trees, and SurvTree. The implementation of the method is publicly available, providing a practical tool for researchers and practitioners. This work advances the field of decision tree-based modeling, offering a more flexible and accurate approach for handling structured data and complex tasks. By leveraging gradient-based optimization, the proposed method bridges the gap between traditional decision trees and modern machine learning techniques, paving the way for further innovations in interpretable and high-performing models.
Battery degradation significantly impacts the reliability and efficiency of energy storage systems, particularly in electric vehicles and industrial applications. Predicting the remaining useful life (RUL) of lithium-ion batteries is crucial for optimizing maintenance schedules, reducing costs, and improving safety. Traditional RUL prediction methods often struggle with nonlinear degradation patterns and uncertainty quantification. To address these challenges, we propose a hybrid survival analysis framework integrating survival data reconstruction, survival model learning, and survival probability estimation. Our approach transforms battery voltage time series into time-to-failure data using path signatures. The multiple Cox-based survival models and machine-learning-based methods, such as DeepHit and MTLR, are learned to predict battery failure-free probabilities over time. Experiments conducted on the Toyota battery and NASA battery datasets demonstrate the effectiveness of our approach, achieving high time-dependent AUC and concordance index (C-Index) while maintaining a low integrated Brier score. The data and source codes for this work are available to the public at https://github.com/thinkxca/rul.
In survival analysis, estimating the conditional survival function given predictors is often of interest. There is a growing trend in the development of deep learning methods for analyzing censored time-to-event data, especially when dealing with high-dimensional predictors that are complexly interrelated. Many existing deep learning approaches for estimating the conditional survival functions extend the Cox regression models by replacing the linear function of predictor effects by a shallow feed-forward neural network while maintaining the proportional hazards assumption. Their implementation can be computationally intensive due to the use of the full dataset at each iteration because the use of batch data may distort the at-risk set of the partial likelihood function. To overcome these limitations, we propose a novel deep learning approach to non-parametric estimation of the conditional survival functions using the generative adversarial networks leveraging self-consistent equations. The proposed method is model-free and does not require any parametric assumptions on the structure of the conditional survival function. We establish the convergence rate of our proposed estimator of the conditional survival function. In addition, we evaluate the performance of the proposed method through simulation studies and demonstrate its application on a real-world dataset.
Leveraging multimodal data, particularly the integration of whole-slide histology images (WSIs) and transcriptomic profiles, holds great promise for improving cancer survival prediction. However, excessive redundancy in multimodal data can degrade model performance. In this paper, we propose Adaptive Prototype Learning (APL), a novel and effective approach for multimodal cancer survival analysis. APL adaptively learns representative prototypes in a data-driven manner, reducing redundancy while preserving critical information. Our method employs two sets of learnable query vectors that serve as a bridge between high-dimensional representations and survival prediction, capturing task-relevant features. Additionally, we introduce a multimodal mixed self-attention mechanism to enable cross-modal interactions, further enhancing information fusion. Extensive experiments on five benchmark cancer datasets demonstrate the superiority of our approach over existing methods. The code is available at https://github.com/HongLiuuuuu/APL.
Histopathology and transcriptomics are fundamental modalities in oncology, encapsulating the morphological and molecular aspects of the disease. Multi-modal self-supervised learning has demonstrated remarkable potential in learning pathological representations by integrating diverse data sources. Conventional multi-modal integration methods primarily emphasize modality alignment, while paying insufficient attention to retaining the modality-specific structures. However, unlike conventional scenarios where multi-modal inputs share highly overlapping features, histopathology and transcriptomics exhibit pronounced heterogeneity, offering orthogonal yet complementary insights. Histopathology provides morphological and spatial context, elucidating tissue architecture and cellular topology, whereas transcriptomics delineates molecular signatures through gene expression patterns. This inherent disparity introduces a major challenge in aligning them while maintaining modality-specific fidelity. To address these challenges, we present MIRROR, a novel multi-modal representation learning method designed to foster both modality alignment and retention. MIRROR employs dedicated encoders to extract comprehensive features for each modality, which is further complemented by a modality alignment module to achieve seamless integration between phenotype patterns and molecular profiles. Furthermore, a modality retention module safeguards unique attributes from each modality, while a style clustering module mitigates redundancy and enhances disease-relevant information by modeling and aligning consistent pathological signatures within a clustering space. Extensive evaluations on TCGA cohorts for cancer subtyping and survival analysis highlight MIRROR's superior performance, demonstrating its effectiveness in constructing comprehensive oncological feature representations and benefiting the cancer diagnosis.
Conventional survival metrics, such as Harrell's concordance index (CI) and the Brier Score, rely on the independent censoring assumption for valid inference with right-censored data. However, in the presence of so-called dependent censoring, where the probability of censoring is related to the event of interest, these metrics can give biased estimates of the underlying model error. In this paper, we introduce three new evaluation metrics for survival analysis based on Archimedean copulas that can account for dependent censoring. We also develop a framework to generate realistic, semi-synthetic datasets with dependent censoring to facilitate the evaluation of the metrics. Our experiments in synthetic and semi-synthetic data demonstrate that the proposed metrics can provide more accurate estimates of the model error than conventional metrics under dependent censoring.
This paper provides a comprehensive analysis of variational inference in latent variable models for survival analysis, emphasizing the distinctive challenges associated with applying variational methods to survival data. We identify a critical weakness in the existing methodology, demonstrating how a poorly designed variational distribution may hinder the objective of survival analysis tasks--modeling time-to-event distributions. We prove that the optimal variational distribution, which perfectly bounds the log-likelihood, may depend on the censoring mechanism. To address this issue, we propose censor-dependent variational inference (CDVI), tailored for latent variable models in survival analysis. More practically, we introduce CD-CVAE, a V-structure Variational Autoencoder (VAE) designed for the scalable implementation of CDVI. Further discussion extends some existing theories and training techniques to survival analysis. Extensive experiments validate our analysis and demonstrate significant improvements in the estimation of individual survival distributions.
Survival analysis, a foundational tool for modeling time-to-event data, has seen growing integration with machine learning (ML) approaches to handle the complexities of censored data and time-varying risks. Despite these advances, leveraging state-of-the-art survival models remains a challenge due to the fragmented nature of existing implementations, which lack standardized interfaces and require extensive preprocessing. We introduce SurvHive, a Python-based framework designed to unify survival analysis methods within a coherent and extensible interface modeled on scikit-learn. SurvHive integrates classical statistical models with cutting-edge deep learning approaches, including transformer-based architectures and parametric survival models. Using a consistent API, SurvHive simplifies model training, evaluation, and optimization, significantly reducing the barrier to entry for ML practitioners exploring survival analysis. The package includes enhanced support for hyper-parameter tuning, time-dependent risk evaluation metrics, and cross-validation strategies tailored to censored data. With its extensibility and focus on usability, SurvHive provides a bridge between survival analysis and the broader ML community, facilitating advancements in time-to-event modeling across domains. The SurvHive code and documentation are available freely at https://github.com/compbiomed-unito/survhive.
Whole slide image (WSI) analysis presents significant computational challenges due to the massive number of patches in gigapixel images. While transformer architectures excel at modeling long-range correlations through self-attention, their quadratic computational complexity makes them impractical for computational pathology applications. Existing solutions like local-global or linear self-attention reduce computational costs but compromise the strong modeling capabilities of full self-attention. In this work, we propose Querent, i.e., the query-aware long contextual dynamic modeling framework, which maintains the expressive power of full self-attention while achieving practical efficiency. Our method adaptively predicts which surrounding regions are most relevant for each patch, enabling focused yet unrestricted attention computation only with potentially important contexts. By using efficient region-wise metadata computation and importance estimation, our approach dramatically reduces computational overhead while preserving global perception to model fine-grained patch correlations. Through comprehensive experiments on biomarker prediction, gene mutation prediction, cancer subtyping, and survival analysis across over 10 WSI datasets, our method demonstrates superior performance compared to the state-of-the-art approaches. Code will be made available at https://github.com/dddavid4real/Querent.