{"type":"ScholarlyArticle","title":"Learning Survival Distribution with Implicit Survival Function","authors":[{"name":"Yu Ling","slug":"yu-ling","given":"Yu","family":"Ling","affiliation":"School of Computer Science , Shanghai Key Laboratory of Intelligent Information Processing , Shanghai Collaborative Innovation Center of Intelligent Visual Computing , Fudan University , Shanghai , China."},{"name":"Weimin Tan","slug":"weimin-tan","given":"Weimin","family":"Tan","affiliation":"School of Computer Science , Shanghai Key Laboratory of Intelligent Information Processing , Shanghai Collaborative Innovation Center of Intelligent Visual Computing , Fudan University , Shanghai , China."},{"name":"Bo Yan","slug":"bo-yan","given":"Bo","family":"Yan","affiliation":"School of Computer Science , Shanghai Key Laboratory of Intelligent Information Processing , Shanghai Collaborative Innovation Center of Intelligent Visual Computing , Fudan University , Shanghai , China."}],"abstract":"Survival analysis aims at modeling the relationship between covariates and event occurrence with some untracked (censored) samples. In implementation, existing methods model the survival distribution with strong assumptions or in a discrete time space for likelihood estimation with censorship, which leads to weak generalization. In this paper, we propose Implicit Survival Function (ISF) based on Implicit Neural Representation for survival distribution estimation without strong assumptions, and employ numerical integration to approximate the cumulative distribution function for prediction and optimization. Experimental results show that ISF outperforms the state-of-the-art methods in three public datasets and has robustness to the hyperparameter controlling estimation precision.","doi":"10.24963/ijcai.2023/442","url":"https://ijcai.org/proceedings/2023/442","pdf":"https://ijcai.org/proceedings/2023/0442.pdf","markdown":"https://ijcai.org/proceedings/2023/442.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/442","volume":{"slug":"2023","title":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2023","url":"https://ijcai.org/proceedings/2023/","year":2023,"location":"Macao, SAR","dates":"19-25 August 2023","editors":"Edith Elkind","isbn":"978-1-956792-03-4","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2023"},"section":"Machine Learning","track":"Main Track","number":442,"pages":{"first":3975,"last":3983},"keywords":["Machine Learning: ML: Other"],"videos":[],"references":[{"position":1,"raw":"[Antolini et al., 2005] Laura Antolini, Patrizia Boracchi, and Elia Biganzoli. A time-dependent discrimination index for survival data. Stats in Medicine, 24(24):3927-3944, 2005.","title":"A time-dependent discrimination index for survival data","authors":"Laura Antolini, Patrizia Boracchi, Elia Biganzoli","year":"2005","venue":"Stats in Medicine","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Chen et al., 2020] Yinbo Chen, Sifei Liu, and Xiaolong Wang. Learning continuous image representation with lo- cal implicit image function. 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 8624-8634, 2020.","title":"Learning continuous image representation with local implicit image function","authors":"Chen","year":"2020","venue":"IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Courtiol et al., 2019] Pierre Courtiol, Charles Maussion, Matahi Moarii, Elodie Pronier, Samuel Pilcer, Meriem Sefta, Pierre Manceron, Sylvain Toldo, Mikhail Za- slavskiy, Nolwenn Le Stang, Nicolas Girard, Olivier El- emento, Andrew G. Nicholson, Jean-Yves Blay, Franc ¸oise Galateau-Sallé, Gilles Wainrib, and Thomas Clozel. Deep learning-based classification of mesothelioma im- proves prediction of patient outcome. Nature Medicine, 25(10):1519-1525, Oct 2019.","title":"Deep learning-based classification of mesothelioma improves prediction of patient outcome","authors":"Courtiol","year":"2019","venue":"Nature Medicine","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Cox, 1992] David R. Cox. Regression Models and Life- Tables, pages 527-541. Springer New York, New York, NY, 1992.","title":"Regression Models and Life-Tables","authors":"R David, Cox","year":"1992","venue":null,"doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Curtis et al., 2012] C. Curtis, Sohrab P. Shah, S. Chin, G. Turashvili, O. Rueda, M. Dunning, D. Speed, A. Lynch, Shamith A. Samarajiwa, Yinyin Yuan, S. Gräf, G. Ha, Gholamreza Haffari, A. Bashashati, R. Russell, S. McK- inney, A. Langerød, A. Green, E. Provenzano, G. Wishart, S. Pinder, P. Watson, F. Markowetz, L. Murphy, I. Ellis, A. Purushotham, A. Børresen-Dale, J. Brenton, S. Tavaré, C. Caldas, and S. Aparicio. The genomic and transcrip- tomic architecture of 2,000 breast tumours reveals novel subgroups. Nature, 486:346 -352, 2012.","title":"The genomic and transcriptomic architecture of 2,000 breast tumours reveals novel subgroups","authors":"C Curtis, P Sohrab, S Shah, G Chin, O Turashvili, M Rueda, D Dunning, A Speed, Shamith A Lynch, Yinyin Samarajiwa, S Yuan, G Gräf, Gholamreza Ha, A Haffari, R Bashashati, S Russell, A Mckinney, A Langerød, E Green, G Provenzano, S Wishart, P Pinder, F Watson, L Markowetz, I Murphy, A Ellis, A Purushotham, J Børresen-Dale, S Brenton, C Tavaré, S Caldas, Aparicio","year":"2012","venue":"Nature","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Doksum and Hóyland, 1992] Kjell A. Doksum and Arnljot Hóyland. Models for variable-stress accelerated life test- ing experiments based on wiener processes and the inverse gaussian distribution. Technometrics, 34(1):74-82, 1992.","title":"Models for variable-stress accelerated life testing experiments based on wiener processes and the inverse gaussian distribution","authors":"A Kjell, Arnljot Doksum, Hóyland","year":"1992","venue":"Technometrics","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Harrell et al., 1982] Jr Harrell, Frank E., Robert M. Califf, David B. Pryor, Kerry L. Lee, and Robert A. Rosati. Eval- uating the Yield of Medical Tests. JAMA, 247(18):2543- 2546, 1982.","title":"Evaluating the Yield of Medical Tests","authors":"Jr Harrell, Frank E Robert, M Califf, David B Pryor, Kerry L Lee, Robert A Rosati","year":"1982","venue":"JAMA","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Hochreiter and Schmidhuber, 1997] Sepp Hochreiter and Jürgen Schmidhuber. Long short-term memory. Neural Comput., 9(8):1735-1780, 1997.","title":"Long short-term memory","authors":"Sepp Hochreiter, Jürgen Schmidhuber","year":"1997","venue":"Neural Comput","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Ishwaran et al., 2008] Hemant Ishwaran, Udaya B. Kogalur, Eugene H. Blackstone, and Michael S. Lauer. Random sur- vival forests. The Annals of Applied Statistics, 2(3):841- 860, 2008.","title":"Random survival forests","authors":"Hemant Ishwaran, B Udaya, Eugene H Kogalur, Michael S Blackstone, Lauer","year":"2008","venue":"The Annals of Applied Statistics","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Jing and Smola, 2017] How Jing and Alexander J. Smola. Neural survival recommender. In Proceedings of the Tenth ACM International Conference on Web Search and Data Mining, WSDM '17, page 515-524, New York, NY, USA, 2017. Association for Computing Machinery.","title":"Neural survival recommender","authors":"Smola Jing, How Jing, Alexander J Smola","year":"2017","venue":"Proceedings of the Tenth ACM International Conference on Web Search and Data Mining, WSDM '17","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Katzman et al., 2018] Jared L. Katzman, Uri Shaham, Alexander Cloninger, Jonathan Bates, Tingting Jiang, and Yuval Kluger. Deepsurv: personalized treatment recom- mender system using a cox proportional hazards deep neural network. BMC Medical Research Methodology, 18(1):24, Feb 2018.","title":"Deepsurv: personalized treatment recommender system using a cox proportional hazards deep neural network","authors":"Jared L Katzman, Uri Shaham, Alexander Cloninger, Jonathan Bates, Tingting Jiang, Yuval Kluger","year":"2018","venue":"BMC Medical Research Methodology","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Knaus et al., 1995] William A. Knaus, Frank Harrell, Joanne Lynn, Lee M. Goldman, Russell S. Phillips, Al- fred F. Connors, Neal V. Dawson, William J. Fulker- son, Robert Califf, Norman A. Desbiens, Peter M. Layde, RobertK. Oye, Paul E. Bellamy, Rosemarie B. Hakim, and Douglas P. Wagner. The support prognostic model: Ob- jective estimates of survival for seriously ill hospitalized adults. Annals of Internal Medicine, 122:191-203, 1995.","title":"The support prognostic model: Objective estimates of survival for seriously ill hospitalized adults","authors":"William A Knaus, Frank Harrell, Joanne Lynn, Lee M Goldman, Russell S Phillips, Alfred F Connors, Neal V Dawson, William J Fulkerson, Robert Califf, Norman A Desbiens, Peter M Layde, Robertk Oye, Paul E Bellamy, Rosemarie B Hakim, Douglas P Wagner","year":"1995","venue":"Annals of Internal Medicine","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Lee and Wang, 2003] Elisa T. Lee and John Wenyu Wang. Statistical Methods for Survival Data Analysis, volume 476. Wiley Publishing, 2003.","title":"Statistical Methods for Survival Data Analysis","authors":"Elisa T Lee, John Wenyu, Wang","year":"2003","venue":null,"doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Lee et al., 2018] Changhee Lee, William R. Zame, Jinsung Yoon, and Mihaela van der Schaar. Deephit: A deep learn- ing approach to survival analysis with competing risks. AAAI, pages 2314-2321, 2018.","title":"Deephit: A deep learning approach to survival analysis with competing risks","authors":"Lee","year":"2018","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Li et al., 2016] Yan Li, Jie Wang, Jieping Ye, and Chan- dan K. Reddy. A multi-task learning formulation for sur- vival analysis. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD '16, page 1715-1724, New York, NY, USA, 2016. Association for Computing Machinery.","title":"A multi-task learning formulation for survival analysis","authors":"Yan Li, Jie Wang, Jieping Ye, Chandan K Reddy","year":"2016","venue":"Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD '16","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Li et al., 2019] Hongming Li, Pamela Boimel, James Janopaul-Naylor, Haoyu Zhong, Ying Xiao, Edgar Ben- Josef, and Yong Fan. Deep convolutional neural networks for imaging data based survival analysis of rectal cancer. IEEE International Symposium on Biomedical Imaging, pages 846-849, 2019.","title":"Deep convolutional neural networks for imaging data based survival analysis of rectal cancer","authors":"Hongming Li, Pamela Boimel, James Janopaul-Naylor, Haoyu Zhong, Ying Xiao, Edgar Ben-Josef, Yong Fan","year":"2019","venue":"IEEE International Symposium on Biomedical Imaging","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Longini et al., 1989] Ira M. Longini, W. Scott Clark, Robert H. Byers, John W. Ward, William W. Darrow, George F. Lemp, and Herbert W. Hethcote. Statistical anal- ysis of the stages of hiv infection using a markov model. Statistics in Medicine, 8(7):831-843, 1989.","title":"Statistical analysis of the stages of hiv infection using a markov model","authors":"Ira M Longini, W Scott Clark, Robert H Byers, John W Ward, William W Darrow, George F Lemp, Herbert W Hethcote","year":"1989","venue":"Statistics in Medicine","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Mildenhall et al., 2020] Ben Mildenhall, Pratul P. Srini- vasan, Matthew Tancik, Jonathan T. Barron, Ravi Ra- mamoorthi, and Ren Ng. Nerf: Representing scenes as neural radiance fields for view synthesis. In European Conference on Computer Vision, 2020.","title":"Nerf: Representing scenes as neural radiance fields for view synthesis","authors":"Ben Mildenhall, P Pratul, Matthew Srinivasan, Jonathan T Tancik, Ravi Barron, Ren Ramamoorthi, Ng","year":"2020","venue":"European Conference on Computer Vision","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Nagpal et al., 2021] Chirag Nagpal, Xinyu Li, and Artur Dubrawski. Deep survival machines: Fully parametric sur- vival regression and representation learning for censored data with competing risks. IEEE Journal of Biomedical and Health Informatics, 25(8):3163-3175, 2021.","title":"Deep survival machines: Fully parametric survival regression and representation learning for censored data with competing risks","authors":"Chirag Nagpal, Xinyu Li, Artur Dubrawski","year":"2021","venue":"IEEE Journal of Biomedical and Health Informatics","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Ranganath et al., 2016] Rajesh Ranganath, Adler Perotte, Noémie Elhadad, and David Blei. Deep survival analysis. Machine Learning for Healthcare Conference, 56:101- 114, 2016.","title":"Deep survival analysis","authors":"Rajesh Ranganath, Adler Perotte, Noémie Elhadad, David Blei","year":"2016","venue":"Machine Learning for Healthcare Conference","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Ren et al., 2019] Kan Ren, Jiarui Qin, Lei Zheng, Zhengyu Yang, Weinan Zhang, Lin Qiu, and Yong Yu. Deep recur- rent survival analysis. AAAI, 33(1):4798-4805, 2019.","title":"Deep recurrent survival analysis","authors":"Jiarui Kan Ren, Lei Qin, Zhengyu Zheng, Weinan Yang, Lin Zhang, Yong Qiu, Yu","year":"2019","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Tancik et al., 2020] Matthew Tancik, Pratul P. Srinivasan, Ben Mildenhall, Sara Fridovich-Keil, Nithin Raghavan, Utkarsh Singhal, Ravi Ramamoorthi, Jonathan T. Barron, and Ren Ng. Fourier features let networks learn high fre- quency functions in low dimensional domains. In Pro- ceedings of the 34th International Conference on Neural Information Processing Systems, NIPS'20, Red Hook, NY, USA, 2020.","title":"Fourier features let networks learn high frequency functions in low dimensional domains","authors":"Matthew Tancik, P Pratul, Ben Srinivasan, Sara Mildenhall, Nithin Fridovich-Keil, Utkarsh Raghavan, Ravi Singhal, Jonathan T Ramamoorthi, Ren Barron, Ng","year":"2020","venue":"Proceedings of the 34th International Conference on Neural Information Processing Systems, NIPS'20","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"Curran Associates Inc. [Tibshirani, 1997]","title":null,"authors":"Curran Associates, Inc","year":"1997","venue":null,"doi":null,"url":null,"internal_url":null},{"position":24,"raw":"Robert Tibshirani. The lasso method for variable selection in the cox model. Statistics in Medicine, 16(4):385-395, 1997.","title":"The lasso method for variable selection in the cox model","authors":"Robert Tibshirani","year":"1997","venue":"Statistics in Medicine","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Vaswani et al., 2017] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Łukasz Kaiser, and Illia Polosukhin. Attention is all you need. In Proceedings of the 31st International Confer- ence on Neural Information Processing Systems, NIPS'17, pages 6000-6010, Red Hook, NY, USA, 2017.","title":"Attention is all you need","authors":"Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, Illia Polosukhin","year":"2017","venue":"Proceedings of the 31st International Conference on Neural Information Processing Systems, NIPS'17","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Zadeh and Schmid, 2021] Shekoufeh Gorgi Zadeh and Matthias Schmid. Bias in cross-entropy-based training of deep survival networks. IEEE Transactions on Pat- tern Analysis and Machine Intelligence, 43(9):3126-3137, 2021.","title":"Bias in cross-entropy-based training of deep survival networks","authors":"Schmid ; Zadeh, Gorgi Shekoufeh, Matthias Zadeh, Schmid","year":"2021","venue":"IEEE Transactions on Pattern Analysis and Machine Intelligence","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Zadeh Shirazi et al., 2020] Amin Zadeh Shirazi, Eric For- naciari, Narjes Sadat Bagherian, Lisa M. Ebert, Bar- bara Koszyca, and Guillermo A. Gomez. Deepsurvnet: deep survival convolutional network for brain cancer sur- vival rate classification based on histopathological im- ages. Medical & Biological Engineering & Computing, 58(5):1031-1045, May 2020.","title":"Deepsurvnet: deep survival convolutional network for brain cancer survival rate classification based on histopathological images","authors":"Amin Zadeh Shirazi, Eric Fornaciari, Narjes Sadat Bagherian, Lisa M Ebert, Barbara Koszyca, Guillermo A Gomez","year":"2020","venue":"Medical & Biological Engineering & Computing","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Zhu et al., 2016] Xinliang Zhu, Jiawen Yao, and Junzhou Huang. Deep convolutional neural network for survival analysis with pathological images. IEEE International Conference on Bioinformatics and Biomedicine, pages 544-547, 2016.","title":"Deep convolutional neural network for survival analysis with pathological images","authors":"Xinliang Zhu, Jiawen Yao, Junzhou Huang","year":"2016","venue":"IEEE International Conference on Bioinformatics and Biomedicine","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}