diff --git a/book/P1C6_survtsk.qmd b/book/P1C6_survtsk.qmd index 74cb17c..44e6f0d 100644 --- a/book/P1C6_survtsk.qmd +++ b/book/P1C6_survtsk.qmd @@ -254,7 +254,7 @@ These are composed as either: 1. $\hatbh(t)\exp(\hat{\eta})$ if proportional hazards is assumed; or 2. $\hatbh(\exp(-\hat{\eta})t)\exp(-\hat{\eta})$ for accelerated failure time models. -## Beyond single-event +## Beyond single-event {#sec-survtsk-beyond} In @sec-eha, competing risks and multi-state models were introduced with a focus on estimating probability distributions. diff --git a/book/P3C15_svm.qmd b/book/P3C15_svm.qmd index 4e57420..fce6fbd 100644 --- a/book/P3C15_svm.qmd +++ b/book/P3C15_svm.qmd @@ -132,7 +132,8 @@ $$ If no observations are censored then the optimization becomes the regression optimization in (@eq-svm-opt). Note that in SSVMs, the $\epsilon$ parameters are typically removed to better accommodate censoring and to help prevent the same penalization of over- and under-predictions. In contrast to this formulation, one *could* introduce more $\epsilon$ and $C$ parameters to separate between under- and over-predictions and to separate right- and left-censoring, however this leads to eight tunable hyperparameters, which is inefficient and may increase overfitting [@pkgsurvivalsvm; @Land2011]. -The algorithm can be simplified to right-censoring only by removing the second constraint completely for anyone censored: + +If only right-censoring is present in the data then the algorithm can be simplified by removing the second constraint completely for anyone censored: $$ \begin{aligned} @@ -180,10 +181,8 @@ This is visualized in @fig-svm-surv-redux where six observations are sorted by o Starting from right to left, the first pair is made by matching the observation to the first uncensored outcome to the left, this continues to the end. In order for all observations to be used in the optimisation, the algorithm sets the first outcome to be uncensored hence observation $2$ being compared to observation $1$. - ![Van Belle SVM nearest neighbors reduction. Sorted observations are paired with the nearest uncensored outcome 'to the left'. Red squares are uncensored observations and blue circles are censored. The observation with the smallest outcome time is always treated as uncensored.](Figures/svm/comparable.png){#fig-svm-surv-redux fig-alt="x-axis says 'observation', y-axis says 'outcome time'. There are six observations that increase linearly from bottom-left to top-right. The order is: uncensored, censored, uncensored, censored, uncensored, uncensored. Arrows show observation 6 matched with 4, 5 matched with 5, 4 matched with 2, 3 matched with 2, 2 matched with 1." width=500} - Using this reduction, the algorithm becomes $$ @@ -208,6 +207,7 @@ $$ Where $\mu_i$ are again Lagrange multipliers. +There do not appear to be any adaptations to the ranking SSVM for other censoring or truncation types. ### Hybrid SSVMs @@ -241,6 +241,13 @@ $$ where $\mu_i, \mu_i^*, \mu_i'$ are Lagrange multipliers and $K$ is a chosen kernel function, which may have further hyper-parameters to select or tune. +### Competing risks + +As of the time of publication, no SSVMs for competing risks appear to have been published [@Kantidakis2023; @Monterrubio-Gómez2024; @Djangang2025]. +As discussed in @sec-survtsk-beyond, there is not a straightforward concept of time-to-event competing risks predictions so survival time SSVMs are unlikely to be extended to competing risks. +For the ranking SSVMs, theoretically one could use any of the methods to estimate per-cause risk by considering each risk separately and censoring observations that experience a different risk, however this has not been validated in the literature. +Moreover, the risks predicted by SSVMs correspond to an abstract relative risk and not an interpretable hazard function, meaning there is no method to transform these predictions to CIFs or other common competing risks statistics. + ## Conclusion :::: {.callout-warning icon=false} diff --git a/book/_book/Machine-Learning-in-Survival-Analysis.pdf b/book/_book/Machine-Learning-in-Survival-Analysis.pdf index 9574f5a..213770f 100644 Binary files a/book/_book/Machine-Learning-in-Survival-Analysis.pdf and b/book/_book/Machine-Learning-in-Survival-Analysis.pdf differ diff --git a/book/library.bib b/book/library.bib index 8d49325..fd29e6a 100644 --- a/book/library.bib +++ b/book/library.bib @@ -1,17 +1,3 @@ -@article{willems2018correctingdependent, - author = {Willems, {\relax SJW} and Schat, A and {van Noorden}, {\relax MS} and Fiocco, M}, - publisher = {SAGE Publications Ltd STM}, - date = {2018-02}, - doi = {10.1177/0962280216628900}, - issn = {0962-2802}, - journaltitle = {Statistical Methods in Medical Research}, - langid = {english}, - number = {2}, - pages = {323--335}, - title = {Correcting for Dependent Censoring in Routine Outcome Monitoring Data by Applying the Inverse Probability Censoring Weighted Estimator}, - volume = {27}, -} - @article{erdmann2024comparisonnonparametrica, author = {Erdmann, Alexandra and Beyersmann, Jan and Bluhmki, Erich}, date = {2024}, @@ -710,19 +696,6 @@ @article{Aalen1978 volume = {6}, } -@book{aalen2008survivalevent, - author = {Aalen, Odd and Borgan, Ornulf and Gjessing, Hakon}, - location = {New York, NY}, - publisher = {Springer}, - date = {2008-08}, - edition = {2008}, - isbn = {978-0-387-20287-7}, - keywords = {Health Sciences,MATHEMATICS,Medicine,Probability Theory and Stochastic Processes,Quality Control,Quality Control Reliability Safety and Risk,Reliability,Safety and Risk,Statistics for Life Sciences,Statistics for Life Sciences Medicine Health Sciences,Stochastic processes}, - langid = {Englisch}, - shorttitle = {{Survival and Event History Analysis}}, - title = {{Survival and Event History Analysis: A Process Point of View}}, -} - @article{datawbc, author = {{The Benelux C M L Study Group}}, url = {https://doi.org/10.1182/blood.V91.8.2713.2713_2713_2721 https://ashpublications.org/blood/article/91/8/2713/107615/Randomized-Study-on-Hydroxyurea-Alone-Versus}, @@ -1740,6 +1713,17 @@ @article{Georgousopoulou2015 volume = {4}, } +@article{Tibshirani1997, + author = {Tibshirani, Robert}, + date = {1997}, + doi = {10.1002/(SICI)1097-0258(19970228)16:4<385::AID-SIM380>3.0.CO;2-3}, + issn = {02776715}, + journaltitle = {Statistics in Medicine}, + pages = {385--395}, + title = {{The Lasso Method for Variable Selection in the Cox Model}}, + volume = {16}, +} + @article{Oh2018, author = {Oh, Sung Eun and Seo, Sung Wook and Choi, Min-Gew and Sohn, Tae Sung and Bae, Jae Moon and Kim, Sung}, url = {https://doi.org/10.1245/s10434-018-6343-7}, @@ -3001,7 +2985,7 @@ @article{pkgsksurvival volume = {21}, } -@article{Royston2002, +@article{RoystonParmar2002, author = {Royston, Patrick and Parmar, Mahesh K.B.}, date = {2002}, doi = {10.1002/sim.1203}, @@ -5758,57 +5742,19 @@ @article{datahepato @article{Reid1994, author = {Reid, Nancy}, - publisher = {Institute of Mathematical Statistics}, - date = {1994-08}, - doi = {10.1214/ss/1177010394}, - issn = {0883-4237, 2168-8745}, + url = {http://www.jstor.org/stable/2238700%5Cnhttp://projecteuclid.org/euclid.aoms/1177705148}, + date = {1994}, + doi = {10.1214/aos/1176348654}, + eprint = {arXiv:1011.1669v3}, + eprinttype = {arXiv}, + issn = {00905364}, journaltitle = {Statistical Science}, number = {3}, pages = {439--455}, - title = {A {{Conversation}} with {{Sir David Cox}}}, + title = {{A Conversation with Sir David Cox}}, volume = {9}, } -@article{breslowCovarianceAnalysisCensored1974, - author = {Breslow, N.}, - date = {1974}, - doi = {10.2307/2529620}, - eprint = {2529620}, - eprinttype = {jstor}, - issn = {0006-341X}, - journaltitle = {Biometrics}, - number = {1}, - pages = {89--99}, - title = {Covariance {{Analysis}} of {{Censored Survival Data}}}, - volume = {30}, -} - -@article{linBreslowEstimator2007, - author = {Lin, D. Y.}, - date = {2007-12}, - doi = {10.1007/s10985-007-9048-y}, - issn = {1572-9249}, - journaltitle = {Lifetime Data Analysis}, - keywords = {Cox model,Maximum likelihood,Partial likelihood,Proportional hazards,Semiparametric inference,Survival data}, - langid = {english}, - number = {4}, - pages = {471--480}, - title = {On the {{Breslow}} Estimator}, - volume = {13}, -} - -@book{therneau2001modelingsurvival, - author = {Therneau, Terry M. and Grambsch, Patricia M.}, - location = {New York}, - publisher = {Springer}, - date = {2001-09}, - edition = {1st ed. 2000. Corr. 2nd printing 2001}, - isbn = {978-0-387-98784-2}, - langid = {Englisch}, - shorttitle = {{Modeling Survival Data}}, - title = {{Modeling Survival Data: Extending the Cox Model}}, -} - @article{Wachter2017, author = {Wachter, Sandra and Mittelstadt, Brent and Floridi, Luciano}, date = {2017}, @@ -7173,20 +7119,7 @@ @article{Schmid2016 volume = {63}, } -@article{bonnevilleWhyYouShould2024, - author = {Bonneville, Edouard F and {de Wreede}, Liesbeth C and Putter, Hein}, - date = {2024-08}, - doi = {10.1093/jrsssa/qnae056}, - issn = {0964-1998}, - journaltitle = {Journal of the Royal Statistical Society Series A: Statistics in Society}, - number = {3}, - pages = {580--593}, - shorttitle = {Why You Should Avoid Using Multiple {{Fine}}--{{Gray}} Models}, - title = {Why You Should Avoid Using Multiple {{Fine}}--{{Gray}} Models: Insights from (Attempts at) Simulating Proportional Subdistribution Hazards Data}, - volume = {187}, -} - -@article{Burk2025, +@article{Burk2024, author = {Burk, Lukas and Zobolas, John and Bischl, Bernd and Bender, Andreas and Wright, Marvin N. and Sonabend, Raphael}, url = {http://arxiv.org/abs/2406.04098}, date = {2024-06}, @@ -7295,7 +7228,7 @@ @article{Monterrubio2024 volume = {66}, } -@article{Austin2022a, +@article{Austin2022, author = {Austin, Peter C and Putter, Hein and Giardiello, Daniele and van Klaveren, David}, url = {https://doi.org/10.1186/s41512-021-00114-6}, date = {2022}, @@ -7491,163 +7424,6 @@ @article{McGough2021 volume = {40}, } -@article{Beaulac2020, - 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pages = {1157--1182}, - title = {An introduction to variable and feature selection}, - volume = {3}, -} - -@article{Bommert2021, - author = {Bommert, Andrea and Welchowski, Thomas and Schmid, Matthias and Rahnenführer, Jörg}, - url = {https://doi.org/10.1093/bib/bbab354}, - date = {2021-09}, - doi = {10.1093/bib/bbab354}, - eprint = {https://academic.oup.com/bib/article-pdf/23/1/bbab354/42229629/bbab354.pdf}, - issn = {1477-4054}, - journaltitle = {Briefings in Bioinformatics}, - number = {1}, - pages = {bbab354}, - title = {Benchmark of filter methods for feature selection in high-dimensional gene expression survival data}, - volume = {23}, -} - @article{Muldowney2012, author = {Muldowney, Pat and Ostaszewski, Krzysztof and Wojdowski, Wojciech}, url = {https://doi.org/10.2478/v10127-012-0025-9}, @@ -7820,6 +7596,302 @@ @inproceedings{Chapfuwa2018 volume = {80}, } +@article{Monterrubio-Gómez2024, + author = {Monterrubio-Gómez, Karla and Constantine-Cooke, Nathan and Vallejos, Catalina A.}, + url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/bimj.202300060}, + date = {2024}, + doi = {https://doi.org/10.1002/bimj.202300060}, + eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/bimj.202300060}, + journaltitle = {Biometrical Journal}, + keywords = {competing risks,risk prediction,survival analysis,time-to-event data}, + number = {2}, + pages = {2300060}, + title = {A review on statistical and machine learning competing risks methods}, + volume = {66}, +} + +@misc{Djangang2025, + author = {Djangang, Paul M. and Han, Summer S. and Sanyal, Nilotpal}, + url = {https://arxiv.org/abs/2503.12824}, + date = {2025}, + eprint = {2503.12824}, + eprintclass = {stat.ME}, + eprinttype = {arXiv}, + title = {Comparative Review of Modern Competing Risk Methods in High-dimensional Settings}, +} + +@article{Kantidakis2023, + author = {Kantidakis, Georgios and Putter, Hein and Litière, Saskia and Fiocco, Marta}, + url = {https://doi.org/10.1186/s12874-023-01866-z}, + date = {2023}, + doi = {10.1186/s12874-023-01866-z}, + issn = {1471-2288}, + issue = {1}, + journaltitle = {BMC Medical Research Methodology}, + pages = {51}, + title = {Statistical models versus machine learning for competing risks: development and validation of prognostic models}, + volume = {23}, +} + +@article{willems2018correctingdependent, + author = {Willems, {\relax SJW} and Schat, A and {van Noorden}, {\relax MS} and Fiocco, M}, + publisher = {SAGE Publications Ltd STM}, + date = {2018-02}, + doi = {10.1177/0962280216628900}, + issn = {0962-2802}, + journaltitle = {Statistical Methods in Medical Research}, + langid = {english}, + number = {2}, + pages = {323--335}, + title = {Correcting for Dependent Censoring in Routine Outcome Monitoring Data by Applying the Inverse Probability Censoring Weighted Estimator}, + volume = {27}, +} + +@book{aalen2008survivalevent, + author = {Aalen, Odd and Borgan, Ornulf and Gjessing, Hakon}, + location = {New York, NY}, + publisher = {Springer}, + date = {2008-08}, + edition = {2008}, + isbn = {978-0-387-20287-7}, + keywords = {Health Sciences,MATHEMATICS,Medicine,Probability Theory and Stochastic Processes,Quality Control,Quality Control Reliability Safety and Risk,Reliability,Safety and Risk,Statistics for Life Sciences,Statistics for Life Sciences Medicine Health Sciences,Stochastic processes}, + langid = {Englisch}, + shorttitle = {{Survival and Event History Analysis}}, + title = {{Survival and Event History Analysis: A Process Point of View}}, +} + +@article{Royston2002, + author = {Royston, Patrick and Parmar, Mahesh K.B.}, + date = {2002}, + doi = {10.1002/sim.1203}, + issn = {02776715}, + journaltitle = {Statistics in Medicine}, + number = {15}, + pages = {2175--2197}, + title = {{Flexible parametric proportional-hazards and proportional-odds models for censored survival data, with application to prognostic modelling and estimation of treatment effects}}, + volume = {21}, +} + +@article{breslowCovarianceAnalysisCensored1974, + author = {Breslow, N.}, + date = {1974}, + doi = {10.2307/2529620}, + eprint = {2529620}, + eprinttype = {jstor}, + issn = {0006-341X}, + journaltitle = {Biometrics}, + number = {1}, + pages = {89--99}, + title = {Covariance {{Analysis}} of {{Censored Survival Data}}}, + volume = {30}, +} + +@article{linBreslowEstimator2007, + author = {Lin, D. 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