{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T21:51:07Z","timestamp":1791323467096,"version":"4.3.1"},"reference-count":69,"publisher":"Institute of Mathematical Statistics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ann. Appl. Stat."],"published-print":{"date-parts":[[2026,9,1]]},"abstract":"Prognostic modeling for lung cancer, a leading cause of mortality, remains a complex task, as it needs to quantify the associations of risk factors and health events spanning a patient\u2019s entire life. One challenge is that an individual\u2019s disease course involves nonterminal (e.g., disease progression) and terminal (e.g., death) events, which form semicompeting relationships. Our motivation comes from the Boston Lung Cancer Study, a large lung cancer survival cohort, which investigates how risk factors influence a patient\u2019s disease trajectory. Following developments in the prediction of time-to-event outcomes with neural networks, deep learning has become a focal area for the development of risk prediction methods in survival analysis. However, limited work has been done to predict multistate or semicompeting risk outcomes, in which a patient may experience adverse events such as disease progression prior to death. We propose a neural expectation-maximization algorithm for semi-competing risks to bridge the gap between classical semicompeting survival models and deep learning. Our algorithm enables estimation of the nonparametric baseline hazards of each state transition, predictor risk functions, and the degree of dependence among different transitions, via a multitask deep neural network with transition-specific subarchitectures. We apply our method to the Boston Lung Cancer Study and investigate the impact of clinical and genetic predictors on disease progression and mortality.<\/jats:p>","DOI":"10.1214\/26-aoas2190","type":"journal-article","created":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T15:25:19Z","timestamp":1790609119000},"page":"2453-2473","source":"Crossref","is-referenced-by-count":0,"title":["Deep learning of semicompeting risk data via a new neural expectation-maximization algorithm"],"prefix":"10.1214","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2763-0494","authenticated-orcid":false,"given":"Stephen","family":"Salerno","sequence":"first","affiliation":[{"name":"Bursky School of Public Health, Washington University in St. Louis"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-5966-2310","authenticated-orcid":false,"given":"Zhilin","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, University of Michigan, Ann Arbor"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1720-2760","authenticated-orcid":false,"given":"Yi","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, University of Michigan, Ann Arbor"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"108","reference":[{"key":"40","doi-asserted-by":"crossref","unstructured":"Kim, S.<\/small>, Zeng, D.<\/small>, Chambless, L.<\/small> and Li, Y.<\/small> (2012). 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American Medical Informatics Association."},{"key":"2","doi-asserted-by":"crossref","unstructured":"ABROL, A.<\/small>, FU, Z.<\/small>, SALMAN, M.<\/small>, SILVA, R.<\/small>, DU, Y.<\/small>, PLIS, S.<\/small> and CALHOUN, V.<\/small> (2021). Deep learning encodes robust discriminative neuroimaging representations to outperform standard machine learning. Nat. Commun.<\/i> 12<\/b> 1\u201317.","DOI":"10.1038\/s41467-020-20655-6"},{"key":"4","doi-asserted-by":"publisher","unstructured":"ANDERSEN, P. K.<\/small>, BORGAN, \u00d8.<\/small>, GILL, R. D.<\/small> and KEIDING, N.<\/small> (2012). Statistical Models Based on Counting Processes<\/i>. Springer Science & Business Media.","DOI":"10.1007\/978-1-4612-4348-9"},{"key":"5","doi-asserted-by":"crossref","unstructured":"ASHWORTH, A. B.<\/small>, SENAN, S.<\/small>, PALMA, D. A.<\/small>, RIQUET, M.<\/small>, AHN, Y. C.<\/small>, RICARDI, U.<\/small>, CONGEDO, M. T.<\/small>, GOMEZ, D. R.<\/small>, WRIGHT, G. M.<\/small> et al. (2014). 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Supplemental Code to \u201cDeep learning of semicompeting risk data via a new neural expectation-maximization algorithm.\u201d https:\/\/doi.org\/10.1214\/26-AOAS2190SUPPB<\/a>","DOI":"10.1214\/26-AOAS2190SUPPB"},{"key":"60","unstructured":"SHU, Y.<\/small>, LIU, J.<\/small>, ZENG, X.<\/small>, HONG, H. G.<\/small>, LI, Y.<\/small>, ZHONG, H.<\/small>, MA, L.<\/small> and FU, P.<\/small> (2018). The effect of overhydration on mortality and technique failure among peritoneal dialysis patients: A systematic review and meta-analysis. Blood Purif.<\/i> 46<\/b> 350\u2013358."},{"key":"61","unstructured":"STEVENS, E.<\/small>, ANTIGA, L.<\/small> and VIEHMANN, T.<\/small> (2020). Deep Learning with PyTorch<\/i>: Build, Train, and Tune Neural Networks Using Python Tools<\/i>. Manning."},{"key":"62","doi-asserted-by":"crossref","unstructured":"TJANDRA, D.<\/small>, HE, Y.<\/small> and WIENS, J.<\/small> (2021). A hierarchical approach to multi-event survival analysis. Proc. AAAI Conf. Artif. Intell.<\/i> 35<\/b> 591\u2013599.","DOI":"10.1609\/aaai.v35i1.16138"},{"key":"63","doi-asserted-by":"crossref","unstructured":"TSENG, J.-S.<\/small>, CHIANG, C.-J.<\/small>, CHEN, K.-C.<\/small>, ZHENG, Z.-R.<\/small>, YANG, T.-Y.<\/small>, LEE, W.-C.<\/small>, HSU, K.-H.<\/small>, HUANG, Y.-H.<\/small>, LIU, T.-W.<\/small> et al. (2022). Association of smoking with patient characteristics and outcomes in small cell lung carcinoma, 2011\u20132018. JAMA Netw. Open<\/i> 5<\/b> e224830\u2013e224830.","DOI":"10.1001\/jamanetworkopen.2022.4830"},{"key":"64","unstructured":"VAN STEENKISTE, S.<\/small>, CHANG, M.<\/small>, GREFF, K.<\/small> and SCHMIDHUBER, J.<\/small> (2018). Relational neural expectation maximization: Unsupervised discovery of objects and their interactions. arXiv preprint arXiv:1802.10353<\/a>."},{"key":"65","unstructured":"WANG, Q.<\/small>, FEDERICI, M.<\/small> and VAN HOOF, H.<\/small> (2025). Bridge the inference gaps of neural processes via expectation maximization. arXiv preprint arXiv:2501.03264<\/a>."},{"key":"66","unstructured":"XIE, J.<\/small>, GIRSHICK, R.<\/small> and FARHADI, A.<\/small> (2016). Unsupervised deep embedding for clustering analysis. In International Conference on Machine Learning<\/i> 478\u2013487. PMLR."},{"key":"68","unstructured":"YEGNANARAYANA, B.<\/small> (2009). Artificial Neural Networks<\/i>. PHI Learning Pvt. Ltd."},{"key":"69","doi-asserted-by":"crossref","unstructured":"YUAN, Q.<\/small>, CAI, T.<\/small>, HONG, C.<\/small>, DU, M.<\/small>, JOHNSON, B. E.<\/small>, LANUTI, M.<\/small>, CAI, T.<\/small> and CHRISTIANI, D. C.<\/small> (2021). Performance of a machine learning algorithm using electronic health record data to identify and estimate survival in a longitudinal cohort of patients with lung cancer. JAMA Netw. Open<\/i> 4<\/b> e2114723\u2013e2114723.","DOI":"10.1001\/jamanetworkopen.2021.14723"}],"container-title":["The Annals of Applied Statistics"],"original-title":[],"deposited":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T21:08:56Z","timestamp":1791320936000},"score":1,"resource":{"primary":{"URL":"https:\/\/projecteuclid.org\/journals\/annals-of-applied-statistics\/volume-20\/issue-3\/Deep-learning-of-semicompeting-risk-data-via-a-new-neural\/10.1214\/26-AOAS2190.full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,1]]},"references-count":69,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2026,9,1]]}},"URL":"https:\/\/doi.org\/10.1214\/26-aoas2190","relation":{},"ISSN":["1932-6157","1941-7330"],"issn-type":[{"value":"1932-6157","type":"print"},{"value":"1941-7330","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,1]]}}}