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Deep Learning for Survival Analysis: A Review

Simon Wiegrebe, Philipp Kopper, Raphael Sonabend, Bernd Bischl, Andreas Bender

arXiv:2305.14961v4stat.MLcs.LG

TL;DR

Deep-learning survival analysis has advanced substantially, yet existing methods often address only a limited subset of time-to-event settings. This paper systematically reviews available methods across survival- and deep-learning-related characteristics, finding that outcomes beyond right-censoring and competing risks are rarely addressed. The review is summarized in an open-source interactive table intended for practical use and community updating.

  • Problem

    No general systematic review comprehensively covered deep-learning methods for survival analysis across survival-specific and deep-learning-related aspects.

  • Method

    The paper conducts a comprehensive review of deep-learning survival methods across theoretical, data-related, and application-oriented characteristics.

  • Results

    Outcomes beyond right-censoring and competing risks are rarely addressed, while methodologically innovative approaches often adapt developments from other deep-learning areas.

  • Takeaways & Limitations

    The review’s open-source interactive table helps practitioners gauge methods for specific use cases and researchers identify promising areas for future research.

  • Takeaways & Limitations

    Sample-size calculation for deep-learning survival analysis lacks published research and must account for events, censoring, truncation, competing events, and complex inputs.

Abstract

from arXiv · show

The influx of deep learning (DL) techniques into the field of survival analysis in recent years has led to substantial methodological progress; for instance, learning from unstructured or high-dimensional data such as images, text or omics data. In this work, we conduct a comprehensive systematic review of DL-based methods for time-to-event analysis, characterizing them according to both survival- and DL-related attributes. In summary, the reviewed methods often address only a small subset of tasks relevant to time-to-event data - e.g., single-risk right-censored data - and neglect to incorporate more complex settings. Our findings are summarized in an editable, open-source, interactive table: https://survival-org.github.io/DL4Survival. As this research area is advancing rapidly, we encourage community contribution in order to keep this database up to date.

1 Introduction

Survival analysis estimates partially censored or truncated time-to-event outcomes, with statistical and machine-learning methods providing established foundations. This review addresses the lack of a general systematic overview by comprehensively characterizing deep-learning survival methods across theoretical and data-related dimensions.

  • Motivation: Survival analysis estimates outcome-time distributions when observations are partially censored, truncated, or both.Typical events include death, system failure, or remission.
  • Motivation: Kaplan-Meier, Cox proportional hazards, random survival forests, and boosting methods form important statistical and machine-learning foundations for survival tasks.Machine-learning methods have often outperformed traditional statistical models in predictive power.
  • Motivation: Early neural-network survival models were shallow and restricted to standard settings, whereas most modern deep-learning methods emerged in the late 2010s.The review identifies method publication years in its Main Table.
  • Research gap: Before this work, existing reviews were narrow in scope, focusing on misuse, genomics, cancer survival, glioma, or a few neural-network methods.The authors report no general systematic review of deep-learning survival methods.
  • Contribution: The review characterizes deep-learning survival methods by model class, neural-network architecture, outcome types, and feature-related aspects.Table 1 summarizes the theoretical and practical dimensions considered.

2 Theoretical Concepts and Data-related Aspects

The paper introduces survival-analysis targets, censoring and truncation mechanisms, diverse outcome and feature settings, and common estimation frameworks. These concepts define the data structures and modeling choices needed for time-to-event analysis.

  • Targets of estimation: The survival function gives the probability of surviving beyond time t, while hazard and cumulative hazard describe instantaneous event risk and an intermediate calculation quantity.The survival function is defined from the cumulative distribution function.
  • Outcome types: Discrete-time methods may estimate a discrete hazard and derive survival probabilities across intervals, or directly estimate the probability mass function.Discrete hazards condition event occurrence on remaining event-free at the beginning of an interval.
  • Data and targets: Survival analysis estimates the distribution of event times conditional on observed feature vectors, despite incomplete observation of individual event times.Subjects may have right-, left-, or interval-censored times.
  • Outcome types: Time-to-event data include censoring, truncation, competing risks, multi-state transitions, and recurrent events.Competing risks involve mutually exclusive events, whereas recurrent-event settings allow repeated occurrences of the same event type.
  • Feature-related aspects: Feature-related aspects include time-varying features, time-varying effects, high-dimensional inputs, and multimodal data such as images or clinical text.High-dimensional and multimodal inputs require adapted architectures or specialized information-extraction techniques.
  • Estimation: Cox models impose time-independent multiplicative feature effects on hazard, whereas parametric, piecewise-exponential, and discrete-time models use alternative likelihood or hazard formulations.Cox parameters are estimated through a log-partial-likelihood based on ordered events and risk sets.

3 Deep Learning in Survival Analysis

Early deep-learning survival techniques extended classical statistical survival models with neural networks. More recent approaches retain statistical survival foundations while using neural networks, multimodal learning, and interpretability advances.

  • Historical development: Early deep-learning survival methods from the mid-1990s were usually neural-network extensions of classical survival models.Examples include neural implementations of Cox and piecewise-exponential models.
  • Modern methods: Recent deep-learning survival methods commonly build on established statistical survival approaches while leveraging neural-network advantages.Advances in multimodal learning and interpretability have increased their appeal for survival tasks.

3.1 Inclusion and Exclusion Criteria

The review screened literature using explicit methodological, evaluation, data, and end-to-end learning criteria. The process yielded 61 articles and 61 distinct methods summarized across theoretical and practical characteristics.

  • Screening process: The literature search combined survival-analysis, neural-network or deep-learning, model or method, and performance or evaluation terms.Web of Science was searched with December 31, 2022 as the cutoff date.
  • Inclusion criteria: Included studies had to develop a new deep-learning method rather than merely apply an existing method to new data or contexts.This criterion targeted methodological contributions.
  • Inclusion criteria: Studies required performance evaluation on at least one non-private benchmark dataset using time-to-event metrics such as the C-index or integrated measures.Benchmark evaluation also supported assessment of predictive utility.
  • Inclusion criteria: The review focused on end-to-end neural-network estimation and prediction for time-to-event data, excluding pipelines that used deep learning solely for feature extraction.All model parameters had to be learned within the neural-network architecture.
  • Review corpus: The screening and supplementary-paper process produced 61 articles representing 61 distinct methods.The inclusion, exclusion, and screening process is visualized in Figure 1.
  • Review scope: The 61 methods were summarized across theoretical characteristics of estimation and architecture and practical characteristics of outcomes and features.The Main Table provides the review’s consolidated method summary.

3.2 Architectural Choices

The review describes how neural-network architectures support flexible survival modeling, including nonlinear effects, unstructured data, competing risks, and multimodal inputs. Architectural choices determine how outputs are parameterized and transformed into survival outcomes.

  • Feed-forward neural networks: Feed-forward neural networks model nonlinear feature effects and complex interactions, enabling flexible estimation of hazard rates.Their forward-only architecture can replace conventional predictors in survival models.
  • Convolutional neural networks: CNNs are typically applied to image data, often using transfer learning from large pretrained networks for smaller survival datasets.ResNet18 is given as an example of a pretrained CNN that can be fine-tuned on case-specific data.
  • Recurrent neural networks: RNNs use short-term memory to incorporate temporal information and are therefore suited to sequential data and time-varying features.This makes them useful when longitudinal measurements are present.
  • Integrated predictors: Deep survival models can combine tabular effects, interactions, time variation, and embeddings from unstructured data within a generalized predictor.The predictor includes nonlinear functions of tabular features and learned embeddings from sources such as images or text, followed by a transformation ψ into a hazard or cumulative incidence function.
  • Specialized architectures: Competing-risks architectures use shared and cause-specific subnetworks, while multimodal architectures use separate subnetworks whose representations are reshaped, concatenated, and fused.The two design patterns can also be combined.

3.3 Estimation and Network Architecture

The review categorizes 61 deep-learning survival methods by model class, loss function, parametrization, and neural-network architecture. Cox-based and discrete-time approaches dominate distinct parts of the reviewed landscape, while methods vary in their handling of high-dimensional, unstructured, multimodal, competing-risk, and longitudinal data.

  • Cox-based methods: 26 of the 61 reviewed methods are Cox-based, parametrizing the log-risk function with a neural network and minimizing a Cox loss.These methods are deep-learning modifications or extensions of Cox regression.
  • Cox-based methods: Cox-based methods include extensions for time-varying effects, high-dimensional omics data, and unstructured or multimodal inputs.Eight Cox-based methods focus on unstructured or multimodal input, while more than half focus on high-dimensional data.
  • Discrete-time methods: 19 methods use discrete-time approaches, typically modeling binary event indicators with neural-network parameterizations of discrete hazards and negative log-likelihood losses.Compared with Cox-based methods, discrete-time methods are more heterogeneous in their loss functions and parametrizations.
  • Discrete-time methods: DeepHit directly parameterizes a discrete probability mass function and combines censoring-adjusted likelihood and ranking losses, with extensions for longitudinal data and joint modeling.Dynamic-DeepHit adds an auxiliary step-ahead prediction loss for time-varying features, while TransformerJM combines NLL- and MSE-based losses.
  • Discrete-time methods: Other reviewed methods use recurrent architectures and specialized losses for competing risks, recurrent events, calibration, discrimination, or censored observations.CRESA uses recurrent cumulative incidence functions; DRSA, Kam2021, and DCS use combinations of likelihood, ranking, RPS, or kernel losses.
  • Parametric methods: Parametric methods DeepWeiSurv and DPWTE are Weibull-based, with DeepWeiSurv parameterizing a Weibull mixture and distribution parameters through a feed-forward network.Neither method addresses the outcome types or feature-related aspects described in the review’s data taxonomy.
  • Ranking-based methods: Ranking-based methods use ranking losses either as auxiliary objectives in discrete-time models or as the basis of continuous-time methods.RankDeepSurv combines ranking losses with an extended MSE loss, whereas SSCNN applies a custom ranking-based loss to clinical and histopathology features.
  • Other methods: The remaining methods include active-learning sampling, adversarial learning, smooth C-index optimization, normalizing flows, and quantile-regression neural networks.These approaches use specialized objectives tailored to event-time distributions, multimodal risk prediction, density estimation, or censored quantile regression.

3.4 Supported Survival Tasks

The review finds that DL survival methods cover diverse outcome and feature settings, but support remains uneven across more complex survival tasks and data types.

  • Outcome types: Left-censoring and right-truncation are not explicitly addressed by any reviewed method.Interval-censoring and left-truncation receive limited or indirect support in several methods.
  • Outcome types: Nine methods address competing risks, but none is Cox-based and four use discrete-time approaches.Several methods use cause-specific subnetworks, while survNode, IDNetwork, and DeepPAMM also support multi-state outcomes.
  • Feature-related aspects: Seven methods address time-varying features, including extensions of DeepHit and DSM, CRESA, Ava2020, survNode, DeepPAMM, and TransformerJM.Implementations include long-format conversion and recurrent networks before new feature measurements.
  • Feature-related aspects: Seven methods can model time-varying effects, with four using time-discrete approaches.Architectural strategies include fully connected networks, recurrent networks, time-dependent relative risk, and follow-up-time interactions.
  • Feature-related aspects: Eighteen methods are explicitly designed for high-dimensional data, usually through specialized regularization techniques.The review separately identifies methods intended for unstructured or multimodal features, including CNN-based approaches focused mainly on medical images.
  • Feature-related aspects: PAGE-Net integrates whole-slide images with demographic and genomic data through patch aggregation, while other methods combine images, clinical variables, text, or tabular features.Examples include DAFT’s bidirectional image-tabular fusion and Tho2022’s fusion of electronic patient-record embeddings with clinical features.

3.5 Interpretability

DL survival models generally offer less inherent interpretability than simpler survival models, although several methods expose biological, pathway-based, structured-feature, or post-hoc explanations.

  • Inherent interpretability: Cox-nnet, Cox-PASNet, PAGE-Net, and DeepOmix assign biological meaning to neural-network nodes or layers.These methods connect hidden or pathway-related nodes to surrogate features, genes, pathways, or functional modules.
  • Inherent interpretability: Cox-PASNet and PAGE-Net use pathway layers and partial-derivative rankings to support pathway-based interpretation of genomic data.PAGE-Net additionally identifies survival-relevant features from histopathological whole-slide images.
  • Inherent interpretability: WideAndDeep and Xie2021 retain standard Cox interpretability for structured features or survival prediction, while DeepPAMM provides classical statistical interpretability.DeepPAMM can use orthogonalization to ensure identifiability when necessary.
  • Post-hoc interpretability: Post-hoc explainability methods are potentially applicable to DL survival models, but their adaptation to censoring, truncation, and other outcome types remains unclear.Survival-specific examples include SurvLIME, SurvSHAP(t), SurvNAM, and other feature-importance methods.

3.6 Model Evaluation and Comparison

The review cautions that self-reported benchmark results are often not meaningfully comparable because datasets, preprocessing, metrics, resampling, and reporting practices vary across studies.

  • Metrics: The C-index is the most popular metric reviewed for assessing risk predictions, while the Brier/Graf score evaluates distribution predictions.Right-censored loss and other evaluation details are described as typically underreported.
  • Comparability: Different datasets, preprocessing choices, missing-value handling, resampling strategies, and metric definitions hinder interpretation across articles.Even nominally identical datasets may use different C-index variants or integrated Brier-score windows.
  • Comparability: Selective reporting and researchers’ degrees of freedom further limit direct comparison of reported performance.Relevant choices include datasets, metrics, tuning budgets, and hyperparameter spaces for proposed and competing algorithms.
  • Future benchmarking: Direct comparison of the reviewed methods is not possible, motivating neutral benchmark studies despite their substantial computational and methodological demands.The review notes that DL benchmarks are especially difficult because of high computational requirements and varying general-purpose implementations.

3.7 Sample Size Requirements

Sample-size requirements remain an underdeveloped issue in deep-learning survival analysis. Existing guidance indicates that requirements depend on architecture, data modalities, data-generating processes, and survival-task specifics, while reviewed papers do not explicitly address them.

  • Sample-size considerations require further research specifically for deep-learning survival analysis.
  • Training requirements depend on model architecture, input data modalities, and the assumed data-generating process.
  • Survival-analysis sample-size calculations must account for event counts, censoring, truncation, competing events, and other outcome-specific factors.Power for detecting effects depends on the number of events for a specific transition rather than overall sample size.
  • The reviewed papers do not explicitly address sample-size requirements, and smaller datasets generally reduce the ability to learn and outperform simpler baselines.The Main Table’s minimum dataset-size column addresses applicability rather than formal sample-size requirements.

3.8 Reproducibility

Reproducibility is supported by accessible code and data, but substantial implementation gaps remain. Code is unavailable for 25 methods, while 28 accompanying implementations are one-shot and not packaged for easy use.

  • Code and data accessibility foster open and reproducible research.
  • Code for 25 methods is not publicly accessible.
  • Implementations for 28 methods are one-shot and have not been processed into easy-to-use packages.The paper recommends packaging new methods and integrating them into general-purpose survival machine-learning and benchmarking suites.

4 Conclusion

The review finds that deep-learning survival research has advanced substantially, especially through adaptations of methods from other DL fields, but coverage of complex survival settings and optimization remains limited. It also identifies challenges in numerical optimization, missing-value handling, sample-size research, and reproducibility, while documenting applications concentrated in medical imaging and omics.

  • 4 Conclusion: Most methodologically innovative methods adapt novel computer-vision or NLP techniques to survival-specific applications.These methods generally provide flexible estimation of associations between structured or unstructured features and outcomes.
  • 4 Conclusion: Outcome types beyond right-censoring and competing risks are rarely addressed.
  • 4 Conclusion: Optimization receives little attention, including optimizer choice, hyperparameter tuning, and neural architecture search.Among articles that discuss optimization, Adam is the most common optimizer.
  • 4 Conclusion: Deep-learning survival analysis faces poorly conditioned likelihood losses, numerical instability, and batching challenges that depend on the survival task.These issues are especially relevant for parametric models with feature-dependent distribution parameters and semi-parametric models such as Cox regression.
  • 4 Conclusion: Missing values are rarely discussed, with explicit handling reported only for MultiSurv and SurvNet.
  • 4 Conclusion: Applications primarily estimate patient survival from medical images or multi-omics data, alongside prognostic indices and cancer recurrence.
  • 4 Conclusion: The field has advanced substantially and is expected to benefit from further ML/DL developments, including possible adaptation of diffusion techniques.Because the area is progressing rapidly, the review cannot remain fully exhaustive or up to date; the authors encourage contributions to the open-source table.
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