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REVIEW 3 major objections 5 minor 76 references

A standardized, reproducible benchmarking pipeline can fairly compare competing-risks survival models, and under it simpler regression-based methods remain highly competitive while the deep-learning model DeSurv leads on three of five datas

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

T0 review · deepseek-v4-flash

2026-08-04 00:50 UTC pith:K3BSBBGE

load-bearing objection Careful benchmarking resource for competing-risks models with a sound but unsurprising CifSHAP(t) extension; the empirical rankings are honest but should be read as protocol-specific, not robust. the 3 major comments →

arxiv 2608.00271 v1 pith:K3BSBBGE submitted 2026-07-31 stat.ML cs.LG

A reproducible and extensible framework for benchmarking competing risks survival models

classification stat.ML cs.LG MSC 62N0162N0262H30
keywords competing riskssurvival analysisbenchmarkingcumulative incidence functionmodel calibrationconcordance indexSHAPinterpretability
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Survival models that ignore competing risks overestimate event risk, yet most published comparisons of newer machine-learning methods are not reproducible. This paper builds an open, extensible benchmarking pipeline that puts six competing-risks models—classical regression, random survival forests, and two deep-learning approaches—through the same nested cross-validation, tuning, and evaluation protocol on five real-world datasets. Its main empirical finding is that simpler regression-based methods remain highly competitive, while the deep-learning model DeSurv outperforms the others on integrated Brier score and the Cτ concordance index in three of the five datasets. The paper also introduces CifSHAP(t), a time-dependent SHAP extension that attributes each covariate's contribution to the cumulative incidence function of each competing cause. A sympathetic reader would care because the framework offers a fair way to compare new methods, and the results caution against assuming deep learning automatically beats classical survival models.

Core claim

Under a single evaluation protocol—nested cross-validation with a common time grid, one-hot encoding, and the integrated Brier score as the shared hyperparameter tuning criterion—the paper compares cause-specific Cox, Fine–Gray, penalised Fine–Gray, random survival forests, DeSurv, and DeepHit across five datasets. The central discovery is that simpler regression-based approaches frequently achieved competitive performance, and that DeSurv achieved the best integrated Brier score and Cτ in three of the five datasets, while DeepHit was often the worst. The paper also proposes CifSHAP(t), which decomposes the predicted cumulative incidence function for each cause at each time point into additi

What carries the argument

The load-bearing mechanism is the benchmark pipeline itself: an outer/inner nested cross-validation with stratified folds, parquet storage for interoperability, and a single pre-specified hyperparameter grid per tunable method, with all tuning done to minimise the same integrated Brier score. On top of this sits a common metric suite (calibration plots, ICI, O/E ratio, tdAUC, Cτ and Ctd, Brier/IBS, and decision curves) and the new CifSHAP(t) extension of SurvSHAP(t), which uses Kernel SHAP to approximate per-covariate contributions to the cause-specific CIF over time. The pipeline is what makes the comparison neutral—the paper's stated goal—by removing inconsistencies in preprocessing, predi

Load-bearing premise

The benchmark's model rankings rest on the assumption that the pre-specified hyperparameter grids and the common IBS-based tuning criterion treat every method comparably; if some grids are too narrow or some methods' losses are misaligned with IBS, the reported ordering could be an artifact of the search protocol rather than of model quality.

What would settle it

Re-run the benchmark on METABRIC with substantially wider hyperparameter grids for DeepHit (deeper architectures, more learning-rate choices) and for RSF (more tree sizes), and with tuning criteria set to each method's own loss; if DeepHit no longer ranks worst under IBS and Cτ, the paper's model ranking is grid-dependent. A simpler check: compare each tuned model's IBS against the best IBS achievable across a much denser grid—a large gap for DeepHit would flag grid stinginess.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • New competing-risks methods can be dropped into the same pipeline and compared against six established baselines without re-implementing different preprocessing or metric code.
  • Because simpler regression models stayed competitive and often beat deep learning, future work should treat them as the baseline to beat rather than assuming neural methods dominate.
  • The choice of hyperparameter tuning criterion can change model rankings; reporting the tuning protocol is as important as reporting the metric.
  • CifSHAP(t) lets clinicians and model developers see how a covariate's contribution to cause-specific risk evolves over time, and whether it pushes the CIF up or down for each competing event.
  • Model rankings depend on which metric is used (IBS vs Cτ vs Ctd), so deployment should select a metric matched to the intended clinical use.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The paper's own limitation analysis suggests the rankings are conditional on hyperparameter grid widths; a natural next step is a grid-sensitivity analysis that varies grid generosity per method and checks whether the DeSurv-over-DeepHit ordering persists.
  • Because CifSHAP(t) attributes contributions to the CIF per cause, it could be used to audit fairness in competing-risk settings—e.g., whether a model systematically shifts the predicted breast-cancer-death CIF differently across racial or age subgroups—something the paper does not explore.
  • The framework is currently confined to low-dimensional tabular, right-censored data; extending it to high-dimensional genomic or longitudinal/time-varying covariates would test whether the 'simple models are competitive' finding generalises.
  • The observation that early stopping hurt performance under IBS tuning suggests that common deep-learning training practices may be misaligned with benchmarking protocols; a separate study could isolate early stopping's effect when tuning by the model's own loss.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper proposes an open-source, extensible benchmarking framework for competing-risks survival models, applies it to six models (csCPH, FGR, FGRP, RSF, DeSurv, DeepHit) across five datasets, and evaluates calibration, discrimination, overall prediction error, and clinical utility under nested cross-validation. It also introduces CifSHAP(t), a time-dependent SHAP extension for cumulative incidence functions. The central empirical claims are that the pipeline provides a neutral comparison, that simpler regression-based methods remain competitive, and that DeSurv outperforms on IBS and Cτ in three of five datasets. The paper includes detailed appendices on hyperparameter grids, imputation, supplementary results, and software/Docker support.

Significance. If the benchmark conclusions are robust, the contribution is valuable: a reproducible, Dockerized pipeline with deterministic training, common nested CV, fold storage, and a common tuning criterion directly addresses the reproducibility gap in competing-risks benchmarking, and CifSHAP(t) is a useful model-agnostic interpretability extension. The paper also ships code and empirical verification of the SHAP reconstruction constraints. However, the headline model rankings are conditional on hand-picked grids and a single tuning criterion, and the statistical support for the claimed outperformance is currently weak; the framework's neutrality claim is therefore not yet fully established.

major comments (3)
  1. [§3.6 and Table S3] Hyperparameter search budgets are highly unequal across methods: FGRP has 30 configurations, DeSurv 18, DeepHit 10, and RSF only 4. With IBS as the common tuning criterion, methods with more extensive grids have more opportunity to minimize the evaluation metric. The text acknowledges that performance claims are bound to the chosen grid (§3.6), but no sensitivity analysis over grid width is provided; §4.5 varies only the tuning criterion for DeepHit. This leaves the 'neutral comparison' claim load-bearing on an unquantified fairness assumption. Please add a grid-width sensitivity analysis (e.g., restricted grids for FGRP/DeSurv, or expanded grids for RSF/DeepHit) and report whether the main rankings persist.
  2. [§4.2.2 and Table 4] The claim that 'DeSurv outperformed based on IBS and Cτ in three out of the five datasets' is not supported by the reported uncertainty. Confidence intervals in Table 4 are computed from only 5 outer folds, ignore training-set overlap, and largely overlap between top and bottom models; e.g., METABRIC IBS for DeSurv is 0.1519 [0.1486,0.1561] versus csCPH 0.1550 [0.1487,0.1599] and FGRP 0.1545 [0.1486,0.1592]. No paired comparisons, hypothesis tests, or effect-size analysis is provided. The paper should either temper the outperformance claim to 'differences were not statistically resolvable at fold-level uncertainty' or add a formal comparison (e.g., paired tests across folds with multiplicity control).
  3. [§3.6 and §4.2.2] The evaluation feedback loop is acknowledged ('potentially driving tunable methods towards similar IBS values') but not mitigated. Because IBS is both the tuning criterion and a headline metric, models whose architecture aligns with smooth CIF estimation may be systematically favored, while methods whose native objectives target discrimination or likelihood are disadvantaged. The sensitivity analysis in §4.5 is limited to one method (DeepHit). To support the neutrality claim, the benchmark should report headline metrics under at least one alternative tuning criterion (e.g., model-specific loss or Cτ) for all tunable methods, or show that the relative rankings are stable when the tuning criterion is changed.
minor comments (5)
  1. [§3.6] Typo: 'preformed' should be 'performed'. Also 'laying above' in §4.2.3 should be 'lying above'.
  2. [S1.1.1] Supplementary heading 'Missigness' should be 'Missingness'.
  3. [Table S3] Please add a column or footnote reporting the number of configurations per method; the uneven grid sizes (30, 4, 18, 10) are relevant to interpreting the benchmark and should be explicit.
  4. [§3.5 / S1.5.2] The empirical verification of CifSHAP(t) constraints is reported only for METABRIC DeepHit and a single notebook. Since CifSHAP(t) is a proposed general extension, consider verifying constraints across all models and datasets, or state the scope of the verification more precisely in the main text.
  5. [§4.1] Pairwise agreement is quantified by Pearson correlation, which is not invariant to monotone transformations and may overstate agreement for skewed risk distributions. Consider also reporting rank-based measures (e.g., Spearman) for the RMTL comparisons.

Circularity Check

0 steps flagged

No significant circularity: the benchmark's empirical rankings are conditional results from nested cross-validation, not derived from their inputs by construction.

full rationale

The paper's central claims are empirical benchmark comparisons across five datasets using nested cross-validation. Hyperparameters for tunable models are selected on inner folds via IBS (§3.6), while all reported IBS, Cτ, Ctd, BS and tdAUC values are computed on outer test folds that were not used for tuning. Therefore the reported model rankings are not equal by construction to the tuning objective. The paper explicitly acknowledges the evaluation-feedback risk: 'IBS based comparisons may favour these methods' (§4.2.2) and 'any performance claims are bound to the chosen optimisation grid' (§3.6). This is a limitation of search-protocol fairness and statistical robustness, not circularity. The proposed CifSHAP(t) is a SHAP-based decomposition of the cause-specific CIF, extending the external SurvSHAP(t) framework via Shapley value axioms; its value function is defined from model predictions and evaluated on held-out data, so there is no self-definitional reduction. Self-citations (e.g., Sierra et al. 2025 for C-index variants; Monterrubio-Gómez et al. 2024 for background) are contextual and not load-bearing for the benchmark conclusions. The paper also qualifies its findings: 'The empirical findings presented here are conditional on the specific set up used in our experiments' (§5). No quoted passage exhibits a specific reduction of a claimed prediction to a fitted input or to a self-citation chain.

Axiom & Free-Parameter Ledger

4 free parameters · 3 axioms · 0 invented entities

The central claims rest on hand-chosen experimental design choices (hyperparameter grids, tuning criterion, fold counts) and standard statistical assumptions. No new physical or conceptual entities are introduced beyond the CifSHAP(t) method name.

free parameters (4)
  • Hyperparameter grids (Table S3) = hand-chosen ranges
    Grid ranges for RSF, FGRP, DeSurv, and DeepHit are chosen by the authors; model rankings depend on these ranges.
  • IBS as hyperparameter tuning criterion = IBS
    Selecting the common inner-CV objective as IBS privileges models that optimize well under this metric, affecting headline comparisons.
  • Number of outer/inner CV folds = 5 outer/3 inner (reduced for PBC and Framingham)
    Fold counts affect variance of performance estimates and were chosen ad hoc based on event proportions.
  • CifSHAP(t) approximation settings = background=15% of training data, 100 coalitions, 50 explained patients
    These computational choices affect SHAP value accuracy and are not derived from theory.
axioms (3)
  • standard math Standard survival analysis definitions of hazard, survival, and cumulative incidence function hold.
    Invoked throughout Section 2 and used for all metrics.
  • domain assumption Shapley value framework applies to the cause-specific CIF as a target function.
    CifSHAP(t) assumes the linear decomposition F_k(t|x)=... holds for any model, which is not guaranteed by Shapley axioms alone.
  • domain assumption Censoring is non-informative conditional on covariates.
    Stated in Section 1 as a common assumption, and used by IPCW and pseudo-observation methods.

pith-pipeline@v1.3.0-alltime-deepseek · 39239 in / 6724 out tokens · 58729 ms · 2026-08-04T00:50:26.925197+00:00 · methodology

0 comments
read the original abstract

A wide range of statistical and machine learning methods have been proposed for survival analysis with competing risks, where the occurrence of one event (i.e., cancer death) precludes the occurrence of other events (i.e., cardiovascular disease death). Despite these methodological advances, their systematic evaluation and adoption are limited by the lack of comprehensive, reproducible and extensible benchmarking frameworks. We developed an open-source benchmarking framework for competing risks models that enables their systematic comparison across multiple datasets under different aspects of performance; calibration, discrimination, overall prediction error and clinical utility. We additionally introduce an extension of SHAP for competing risks, allowing model-agnostic interpretability of covariates contributions over time. All our code is publicly available via GitHub:https://github.com/BBolosSierra/CompRisksBenchmark

Figures

Figures reproduced from arXiv: 2608.00271 by Bego\~na B. Sierra, Catalina A. Vallejos, Colin McLean, Peter S. Hall, Sarah Friedrich-Welz.

Figure 1
Figure 1. Figure 1: Overview of our benchmark pipeline for assessing risk prediction performance of CR methods. The workflow begins with [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Pairwise comparison of individual-level predicted CIF at a specific time [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Evaluation with t-year metrics of benchmarked models on METABRIC dataset for cause of interest (cause 1). A) Integrated Calibration Index (ICI) over time, where dotted vertical lines indicate the time grid at which the calibration plots were computed, and subsequently ICI derived from. B) O/E ratio across models for cause of interest at t = 5 years, where deviations from 1 indicate miscalibration at that s… view at source ↗
Figure 4
Figure 4. Figure 4: Evaluation of clinical utility at 5-year for benchmarked models on FRAMINGHAM and SEER datasets for cause of interest (cause 1). Net benefit curves over treat all and treat none indicate positive net benefit at the given threshold probability [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Model benchmark results across datasets for cause 1 for global performance metrics: IBS, [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Covariate ranks across models on METABRIC dataset (rank [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: CifSHAP(t) values for cause 1 stratified by event type on METABRIC dataset for DeSurv (top) and DeepHit (bottom). The SHAP values are calculated per each outer fold, with a background dataset of 400 individuals from the outer training sets, and 50 individuals to be explained derived from the respective outer test. The confidence intervals are calculated across the outer folds. Proportions of events (i.e., … view at source ↗
Figure 8
Figure 8. Figure 8: Training runtime (seconds) of each model on progressively larger samples of SEER dataset. Each point corresponds to [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗

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Reference graph

Works this paper leans on

76 extracted references · 13 canonical work pages

  1. [1]

    2022 , doi =

    van Geloven, Nan and Giardiello, Daniele and Bonneville, Edouard F and Teece, Lucy and Ramspek, Chava L and van Smeden, Maarten and Snell, Kym I E and van Calster, Ben and Pohar-Perme, Maja and Riley, Richard D and Putter, Hein and Steyerberg, Ewout , title =. 2022 , doi =. https://www.bmj.com/content/377/bmj-2021-069249.full.pdf , journal =

  2. [2]

    Austin and Douglas S

    Peter C. Austin and Douglas S. Lee and Jason P. Fine , title =. Circulation , volume =. 2016 , doi =. https://www.ahajournals.org/doi/pdf/10.1161/CIRCULATIONAHA.115.017719 , abstract =

  3. [3]

    Journal of the American Statistical Association , volume=

    A proportional hazards model for the subdistribution of a competing risk , author=. Journal of the American Statistical Association , volume=. 1999 , publisher=

  4. [4]

    Journal of the Royal Statistical Society: Series B (Methodological) , volume=

    Regression models and life-tables , author=. Journal of the Royal Statistical Society: Series B (Methodological) , volume=. 1972 , publisher=

  5. [5]

    Deep learning for survival analysis: a review , volume=

    Wiegrebe, Simon and Kopper, Philipp and Sonabend, Raphael and Bischl, Bernd and Bender, Andreas , year=. Deep learning for survival analysis: a review , volume=. Artificial Intelligence Review , publisher=. doi:10.1007/s10462-023-10681-3 , number=

  6. [6]

    , title =

    Monterrubio-Gómez, Karla and Constantine-Cooke, Nathan and Vallejos, Catalina A. , title =. Biometrical Journal , volume =. doi:https://doi.org/10.1002/bimj.202300060 , url =. https://onlinelibrary.wiley.com/doi/pdf/10.1002/bimj.202300060 , abstract =

  7. [7]

    Proceedings of the 2nd Machine Learning for Healthcare Conference , pages =

    Reproducibility in critical care: a mortality prediction case study , author =. Proceedings of the 2nd Machine Learning for Healthcare Conference , pages =. 2017 , editor =

  8. [8]

    and Raatz, Heike and Steyerberg, Ewout W

    Koller, Michael T. and Raatz, Heike and Steyerberg, Ewout W. and Wolbers, Marcel , title =. Statistics in Medicine , volume =. doi:https://doi.org/10.1002/sim.4384 , url =. https://onlinelibrary.wiley.com/doi/pdf/10.1002/sim.4384 , abstract =

  9. [9]

    and Meier, Paul , title =

    Kaplan, Edward L. and Meier, Paul , title =. Journal of the American Statistical Association , year =

  10. [10]

    2013 , volume =

    The Cancer Genome Atlas Pan-Cancer analysis project , journal =. 2013 , volume =. doi:10.1038/ng.2764 , url =

  11. [11]

    and Gerds, Thomas A

    Blanche, Paul and Kattan, Michael W. and Gerds, Thomas A. , title =. Biostatistics , volume =. 2019 , month =. doi:10.1093/biostatistics/kxy006 , pmid =

  12. [12]

    Continuous and discrete-time survival prediction with neural networks , journal =

    H. Continuous and discrete-time survival prediction with neural networks , journal =. 2021 , volume =. doi:10.1007/s10985-021-09532-6 , url =

  13. [13]

    and Witteman, Jacqueline C

    Wolbers, Marcel and Blanche, Paul and Koller, Michael T. and Witteman, Jacqueline C. and Gerds, Thomas A. , title =. Biostatistics , volume =. 2014 , month =. doi:10.1093/biostatistics/kxt059 , pmid =

  14. [14]

    and Yoon, Jinsung and van der Schaar, Mihaela , title =

    Lee, Changhee and Zame, William R. and Yoon, Jinsung and van der Schaar, Mihaela , title =. 2018 , booktitle =

  15. [15]

    Edinburgh Compute and Data Facility , year =

  16. [16]

    Stat , volume=

    Survival Conformal Prediction Under Random Censoring , author=. Stat , volume=. 2025 , publisher=

  17. [17]

    Journal of the Royal Statistical Society Series B: Statistical Methodology , volume=

    Conformalized survival analysis , author=. Journal of the Royal Statistical Society Series B: Statistical Methodology , volume=. 2023 , publisher=

  18. [18]

    Advances in neural information processing systems , volume=

    Conformal prediction under covariate shift , author=. Advances in neural information processing systems , volume=

  19. [19]

    Lifetime data analysis , volume=

    On pseudo-values for regression analysis in competing risks models , author=. Lifetime data analysis , volume=. 2009 , publisher=

  20. [20]

    Biometrika , volume=

    Generalised linear models for correlated pseudo-observations, with applications to multi-state models , author=. Biometrika , volume=. 2003 , publisher=

  21. [21]

    Neurocomputing , year =

    On hyperparameter optimization of machine learning algorithms: Theory and practice , author =. Neurocomputing , year =. doi:https://doi.org/10.1016/j.neucom.2020.07.061 , abstract =

  22. [22]

    Journal of Computational Science , year =

    BSense: A parallel Bayesian hyperparameter optimized Stacked ensemble model for breast cancer survival prediction , author =. Journal of Computational Science , year =. doi:https://doi.org/10.1016/j.jocs.2022.101570 , abstract =

  23. [23]

    JCO Clinical Cancer Informatics , volume =

    Multiomic Integration of Public Oncology Databases in Bioconductor , author =. JCO Clinical Cancer Informatics , volume =. 2020 , doi =

  24. [24]

    Nature , volume=

    The genomic and transcriptomic architecture of 2,000 breast tumours reveals novel subgroups , author=. Nature , volume=. 2012 , publisher=. doi:10.1038/nature10983 , url=

  25. [25]

    and Shaham, Uri and Cloninger, Alexander and Bates, Jonathan and Jiang, Tingting and Kluger, Yuval , year=

    Katzman, Jared L. and Shaham, Uri and Cloninger, Alexander and Bates, Jonathan and Jiang, Tingting and Kluger, Yuval , year=. Deep. BMC Medical Research Methodology , publisher=. doi:10.1186/s12874-018-0482-1 , number=

  26. [26]

    risk R egression: Predicting the risk of an event using C ox regression models

    Brice Ozenne and S rensen, Anne Lyngholm and Thomas Scheike and Christian Torp-Pedersen and Gerds, Thomas Alexander. risk R egression: Predicting the risk of an event using C ox regression models. The R Journal. 2017

  27. [27]

    Proceedings of The 25th International Conference on Artificial Intelligence and Statistics , pages =

    Derivative-Based Neural Modelling of Cumulative Distribution Functions for Survival Analysis , author =. Proceedings of The 25th International Conference on Artificial Intelligence and Statistics , pages =. 2022 , editor =

  28. [28]

    Statistical Methods in Medical Research , volume =

    Per Kragh Andersen and Maja Pohar Perme , title =. Statistical Methods in Medical Research , volume =. 2010 , doi =. https://doi.org/10.1177/0962280209105020 , abstract =

  29. [29]

    and Andersen, Per K

    Gerds, Thomas A. and Andersen, Per K. and Kattan, Michael W. , title =. Statistics in Medicine , volume =. doi:https://doi.org/10.1002/sim.6152 , url =. https://onlinelibrary.wiley.com/doi/pdf/10.1002/sim.6152 , abstract =

  30. [30]

    arXiv preprint arXiv:2508.05435 , year =

    Vincent Jeanselme and Brian Tom and Jessica Barrett , title =. arXiv preprint arXiv:2508.05435 , year =

  31. [31]

    Christian Marius Lillelund and Shi-ang Qi and Russell Greiner and Christian Fischer Pedersen , year=. Stop. 2506.02075 , archivePrefix=

  32. [32]

    Avoiding

    Sonabend, Raphael and Bender, Andreas and Vollmer, Sebastian , journal=. Avoiding. 2022 , publisher=

  33. [33]

    Bego. The. arXiv preprint arXiv:2508.14821 , year =

  34. [34]

    2020 , doi =

    Whitty, Christopher J M and MacEwen, Carrie and Goddard, Andrew and Alderson, Derek and Marshall, Martin and Calderwood, Catherine and Atherton, Frank and McBride, Michael and Atherton, John and Stokes-Lampard, Helen and Reid, Wendy and Powis, Stephen and Marx, Clare , title =. 2020 , doi =. https://www.bmj.com/content/368/bmj.l6964.full.pdf , journal =

  35. [35]

    , title =

    Wang, Ping and Li, Yan and Reddy, Chandan K. , title =. ACM Computing Surveys , year =

  36. [36]

    PLOS ONE , publisher =

    A Plea for Neutral Comparison Studies in Computational Sciences , year =. PLOS ONE , publisher =. doi:10.1371/journal.pone.0061562 , author =

  37. [37]

    and Parikh, C

    Fu, Z. and Parikh, C. R. and Zhou, B. , title =. Lifetime Data Analysis , year =. doi:10.1007/s10985-016-9362-3 , url =

  38. [38]

    and Blackstone, Eugene H

    Ishwaran, Hemant and Kogalur, Udaya B. and Blackstone, Eugene H. and Lauer, Michael S. , year=. Random survival forests , volume=. The Annals of Applied Statistics , publisher=. doi:10.1214/08-aoas169 , number=

  39. [39]

    Aalen and Søren Johansen , journal =

    Odd O. Aalen and Søren Johansen , journal =. An Empirical Transition Matrix for Non-Homogeneous Markov Chains Based on Censored Observations , urldate =

  40. [40]

    2025 , url =

    Apache Parquet , author =. 2025 , url =

  41. [41]

    and Lee, Su-In , title =

    Lundberg, Scott M. and Lee, Su-In , title =. Proceedings of the 31st International Conference on Neural Information Processing Systems , pages =. 2017 , isbn =

  42. [42]

    Mateusz Krzyziński and Mikołaj Spytek and Hubert Baniecki and Przemysław Biecek , keywords =. Surv. Knowledge-Based Systems , volume =. 2023 , issn =. doi:https://doi.org/10.1016/j.knosys.2022.110234 , url =

  43. [43]

    2025 , note =

    kernelshap: Kernel SHAP , author =. 2025 , note =

  44. [44]

    arXiv preprint arXiv:2602.00194 , year =

    Julie Alberge and Tristan Haugomat and Gaël Varoquaux and Judith Abécassis , title =. arXiv preprint arXiv:2602.00194 , year =

  45. [45]

    Wright and Raphael Sonabend , title =

    Lukas Burk and John Zobolas and Bernd Bischl and Andreas Bender and Marvin N. Wright and Raphael Sonabend , title =. arXiv preprint arXiv:2406.04098 , year =

  46. [46]

    Djangang and Summer S

    Paul M. Djangang and Summer S. Han and Nilotpal Sanyal , title =. arXiv preprint arXiv:2503.12824 , year =

  47. [47]

    Comparison of statistical and machine learning methods in competing risk analysis , volume =

    Lee, Ji and Shin, Insu and Lee, Jae-Woo , year =. Comparison of statistical and machine learning methods in competing risk analysis , volume =. Communications for Statistical Applications and Methods , doi =

  48. [48]

    and Kogalur, Udaya B

    Ishwaran, Hemant and Gerds, Thomas A. and Kogalur, Udaya B. and Moore, Richard D. and Gange, Stephen J. and Lau, Bryan M. , title =. Biostatistics , volume =. 2014 , month =. doi:10.1093/biostatistics/kxu010 , url =

  49. [49]

    Journal of Statistical Software , year =

    Stef. Journal of Statistical Software , year =

  50. [50]

    Kalbfleisch, J. D. and Prentice, R. L. , biburl =. The

  51. [51]

    2017 , edition=

    Absolute Risk: Methods and Applications in Clinical Management and Public Health , author=. 2017 , edition=. doi:10.1201/9781315117539 , isbn=

  52. [52]

    and Schumacher, Martin , title =

    Gerds, Thomas A. and Schumacher, Martin , title =. Biometrical Journal , volume =. doi:https://doi.org/10.1002/bimj.200610301 , url =. https://onlinelibrary.wiley.com/doi/pdf/10.1002/bimj.200610301 , abstract =

  53. [53]

    2017 , doi =

    Hippisley-Cox, Julia and Coupland, Carol and Brindle, Peter , title =. 2017 , doi =. https://www.bmj.com/content/357/bmj.j2099.full.pdf , journal =

  54. [54]

    and Griffith, John and Tighiouart, Hocine and Djurdjev, Ognjenka and Naimark, David and Levin, Adeera and Levey, Andrew S

    Tangri, Navdeep and Stevens, Lesley A. and Griffith, John and Tighiouart, Hocine and Djurdjev, Ognjenka and Naimark, David and Levin, Adeera and Levey, Andrew S. , title =. JAMA , volume =. 2011 , month =. doi:10.1001/jama.2011.451 , url =

  55. [55]

    2006 , publisher =

    Competing Risks: A Practical Perspective , author =. 2006 , publisher =

  56. [56]

    2025 , howpublished =

    Karla Monterrubio , title =. 2025 , howpublished =

  57. [57]

    2022 , howpublished =

    Nan van Geloven and Daniele Giardiello and Hein Putter and contributors , title =. 2022 , howpublished =

  58. [58]

    Thurston and others , title =

    Jasper Boeddinghaus and Pedro Lopez-Ayala and Alexander J.F. Thurston and others , title =. JACC , volume =. 2026 , doi =

  59. [59]

    2025 , url =

    R: A Language and Environment for Statistical Computing , author =. 2025 , url =

  60. [60]

    Python Language Reference, version 3.9.16 , author =

    Python Software Foundation. Python Language Reference, version 3.9.16 , author =. 2025 , url =

  61. [61]

    and Shen, Jenny I

    Kawaguchi, Eric S. and Shen, Jenny I. and Li, Gang and Suchard, Marc A. , title =. The R Journal , year =. doi:10.32614/RJ-2021-010 , volume =

  62. [62]

    Statistics in Medicine , volume =

    A time-dependent discrimination index for survival data , author =. Statistics in Medicine , volume =. 2005 , publisher =. doi:10.1002/sim.2427 , url =

  63. [63]

    Journal of the Royal Statistical Society Series C , author=

    A Mixture Model for the Regression Analysis of Competing Risks Data , year=. Journal of the Royal Statistical Society Series C , author=. doi:10.2307/2347464 , url=

  64. [64]

    and D'Agostino, Ralph B

    Uno, Hajime and Cai, Tianxi and Pencina, Michael J. and D'Agostino, Ralph B. and Wei, L. J. , title =. Statistics in Medicine , year =

  65. [65]

    and Heagerty, P

    Saha, P. and Heagerty, P. J. , title =. Biometrics , volume =. 2010 , month =. doi:10.1111/j.1541-0420.2009.01375.x , url =

  66. [66]

    BMC Medical Research Methodology , year =

    Lyu, Jingjing and Hou, Yawen and Chen, Zheng , title =. BMC Medical Research Methodology , year =. doi:10.1186/s12874-020-01040-9 , url =

  67. [67]

    American Journal of Epidemiology , volume =

    Wu, Hongji and Yuan, Hao and Yang, Zijing and Hou, Yawen and Chen, Zheng , title =. American Journal of Epidemiology , volume =. 2022 , month =. doi:10.1093/aje/kwab235 , url =

  68. [68]

    JAMA Cardiology , volume =

    Zhao, Lihui and Tian, Lu and Claggett, Brian and Pfeffer, Marc and Kim, Dae Hyun and Solomon, Scott and Wei, Lee-Jen , title =. JAMA Cardiology , volume =. 2018 , month =. doi:10.1001/jamacardio.2018.0127 , url =

  69. [69]

    Bioinformatics , month =

    mlr3proba: An R Package for Machine Learning in Survival Analysis , author =. Bioinformatics , month =. 2021 , doi =

  70. [70]

    2019 , note =

    Kvamme, Håvard and Borgan, Ørnulf , title =. 2019 , note =

  71. [71]

    Statistical models versus machine learning for competing risks: development and validation of prognostic models , journal =

    Kantidakis, Georgios and Putter, Hein and Liti. Statistical models versus machine learning for competing risks: development and validation of prognostic models , journal =. 2023 , volume =

  72. [72]

    2026 , note =

    A Package for Survival Analysis in R , author =. 2026 , note =

  73. [73]

    PLOS ONE , publisher =

    Introducing risk. PLOS ONE , publisher =. 2022 , month =. doi:10.1371/journal.pone.0265368 , author =

  74. [74]

    2023 , note =

    pec: Prediction Error Curves for Risk Prediction Models in Survival Analysis , author =. 2023 , note =

  75. [75]

    2026 , publisher =

    Hosseini, Mohammad and Kerridge, Simon and Allen, Liz and Kiermer, Veronique and Holmes, Kristi , title =. 2026 , publisher =. doi:10.5281/zenodo.18421449 , url =

  76. [76]

    and Grambsch, Patricia M

    Therneau, Terry M. and Grambsch, Patricia M. , title =. 2000 , isbn =