{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,10]],"date-time":"2026-09-10T16:10:55Z","timestamp":1789056655258,"version":"build-2803163510"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2026,9,10]],"date-time":"2026-09-10T00:00:00Z","timestamp":1788998400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,9,10]],"date-time":"2026-09-10T00:00:00Z","timestamp":1788998400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001734","name":"Copenhagen University","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100001734","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Lifetime Data Anal"],"published-print":{"date-parts":[[2026,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Cure models have become increasingly popular over the last couple of decades. An appealing element of cure models is the idea that part of the population is immune to the event of interest. We argue that, in medical applications, the use of cure models is limited. Thus, true cure cannot exist if the event of interest includes death, as death is inevitable, and if death is excluded then competing risks must be accounted for. In this case, we find it more natural to model the cumulative incidence of both the event of interest and competing events over time, avoiding unreliable estimates at infinity and using observed data. Further, we point out two more technical difficulties with cure models arising, first, from the fact that cure models rely on identifying plateaus in survival curves at the tail, where data may be sparse and unreliable and, second, the mixture cure model faces issues with practical identifiability of covariate effects in the incidence model (probability of cure), especially alongside proportional hazards assumptions in the latency model (survival model, conditionally on not being cured). We also comment on hybrid extensions of the classical single event cure model that allow for both competing risks and a cured fraction. We support our arguments with real and simulated data. Full data and code are available online.<\/jats:p>","DOI":"10.1007\/s10985-026-09729-7","type":"journal-article","created":{"date-parts":[[2026,9,10]],"date-time":"2026-09-10T15:57:10Z","timestamp":1789055830000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["No cure for cure models: killed by competing risks"],"prefix":"10.1007","volume":"32","author":[{"given":"Hein","family":"Putter","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0490-0885","authenticated-orcid":false,"given":"Per Kragh","family":"Andersen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,9,10]]},"reference":[{"issue":"1","key":"9729_CR1","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1146\/annurev-statistics-031017-100101","volume":"5","author":"M Amico","year":"2018","unstructured":"Amico M, van Keilegom I (2018) Cure models in survival analysis. Annu Rev Stat Appl 5(1):311\u2013342","journal-title":"Annu Rev Stat Appl"},{"key":"9729_CR2","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1007\/s10985-008-9097-x","volume":"14","author":"PK Andersen","year":"2008","unstructured":"Andersen PK, Pohar Perme M (2008) Inference for outcome probabilities in multi-state models. Lifetime Data Anal 14:405\u2013431","journal-title":"Lifetime Data Anal"},{"key":"9729_CR3","doi-asserted-by":"publisher","DOI":"10.1201\/9780429029684","volume-title":"Models for multi-state survival data: rates, risks, and pseudo-values","author":"PK Andersen","year":"2023","unstructured":"Andersen PK, Ravn H (2023) Models for multi-state survival data: rates, risks, and pseudo-values. CRC Press"},{"issue":"3","key":"9729_CR4","doi-asserted-by":"publisher","first-page":"861","DOI":"10.1093\/ije\/dyr213","volume":"41","author":"PK Andersen","year":"2012","unstructured":"Andersen PK, Geskus RB, de Witte T, Putter H (2012) Competing risks in epidemiology: possibilities and pitfalls. Int J Epidemiol 41(3):861\u2013870","journal-title":"Int J Epidemiol"},{"issue":"11","key":"9729_CR5","doi-asserted-by":"publisher","first-page":"3424","DOI":"10.1177\/0962280220921889","volume":"29","author":"TA Balan","year":"2020","unstructured":"Balan TA, Putter H (2020) A tutorial on frailty models. Stat Methods Med Res 29(11):3424\u20133454","journal-title":"Stat Methods Med Res"},{"key":"9729_CR6","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1111\/j.1467-985X.2009.00618.x","volume":"173","author":"S Basu","year":"2010","unstructured":"Basu S, Tiwari RC (2010) Breast cancer survival, competing risks and mixture cure model: a Bayesian analysis. J R Stat Soc Ser A 173:307\u2013329","journal-title":"J R Stat Soc Ser A"},{"issue":"3","key":"9729_CR7","doi-asserted-by":"publisher","first-page":"416","DOI":"10.1093\/biostatistics\/kxy011","volume":"20","author":"LJ Beesley","year":"2019","unstructured":"Beesley LJ, Taylor JMG (2019) Em algorithms for fitting multistate cure models. Biostatistics 20(3):416\u2013432","journal-title":"Biostatistics"},{"issue":"259","key":"9729_CR8","doi-asserted-by":"publisher","first-page":"501","DOI":"10.1080\/01621459.1952.10501187","volume":"47","author":"J Berkson","year":"1952","unstructured":"Berkson J, Gage RP (1952) Survival curve for cancer patients following treatment. J Am Stat Assoc 47(259):501\u2013515","journal-title":"J Am Stat Assoc"},{"issue":"1","key":"9729_CR9","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1111\/j.2517-6161.1949.tb00020.x","volume":"11","author":"JW Boag","year":"1949","unstructured":"Boag JW (1949) Maximum likelihood estimates of the proportion of patients cured by cancer therapy. J R Stat Soc Ser B (Methodol) 11(1):15\u201353","journal-title":"J R Stat Soc Ser B (Methodol)"},{"key":"9729_CR10","unstructured":"Cai C, Zou Y, Peng Y, Zhang J (2022) smcure: fit semiparametric mixture cure models. R package version 2:1"},{"key":"9729_CR11","doi-asserted-by":"publisher","first-page":"4086","DOI":"10.1002\/sim.8711","volume":"39","author":"C-M Chen","year":"2020","unstructured":"Chen C-M, Shen P-S, Lin C-C, Wu C-C (2020) Semiparametric mixture cure model analysis with competing risks data: application to vascular access thrombosis data. Stat Med 39:4086\u20134099","journal-title":"Stat Med"},{"key":"9729_CR12","doi-asserted-by":"publisher","first-page":"1750","DOI":"10.1002\/sim.6056","volume":"33","author":"ASC Conlon","year":"2013","unstructured":"Conlon ASC, Taylor JMG, Sargent DJ (2013) Multi-state models for colon cancer recurrence and death with a cured fraction. Stat Med 33:1750\u20131766","journal-title":"Stat Med"},{"issue":"3","key":"9729_CR13","doi-asserted-by":"publisher","first-page":"403","DOI":"10.2307\/2297364","volume":"49","author":"C Elbers","year":"1982","unstructured":"Elbers C, Ridder G (1982) True and spurious duration dependence: the identifiability of the proportional hazard model. Rev Econ Stud 49(3):403\u2013409","journal-title":"Rev Econ Stud"},{"issue":"5","key":"9729_CR14","doi-asserted-by":"publisher","first-page":"742","DOI":"10.1097\/EDE.0000000000000130","volume":"25","author":"S Eloranta","year":"2014","unstructured":"Eloranta S, Lambert PC, Andersson TM-L, Bj\u00f6rkholm M, Dickmann PW (2014) The application of cure models in the presence of competing risks. A tool for improved risk communication in population-based cancer patient survival. Epidemiology 25(5):742\u2013748","journal-title":"Epidemiology"},{"issue":"4","key":"9729_CR15","doi-asserted-by":"publisher","first-page":"1041","DOI":"10.2307\/2529885","volume":"38","author":"VT Farewell","year":"1982","unstructured":"Farewell VT (1982) The use of mixture models for the analysis of survival data with long-term survivors. Biometrics 38(4):1041\u20131046","journal-title":"Biometrics"},{"issue":"296","key":"9729_CR16","doi-asserted-by":"publisher","first-page":"841","DOI":"10.1080\/01621459.1961.10482130","volume":"56","author":"LA Goodman","year":"1961","unstructured":"Goodman LA (1961) Statistical methods for the mover-stayer model. J Am Stat Assoc 56(296):841\u2013868","journal-title":"J Am Stat Assoc"},{"key":"9729_CR17","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1016\/j.jmva.2014.06.002","volume":"130","author":"L Hanin","year":"2014","unstructured":"Hanin L, Huang L-S (2014) Identifiability of cure models revisited. J Multivar Anal 130:261\u2013274","journal-title":"J Multivar Anal"},{"key":"9729_CR18","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1111\/j.0006-341X.2001.00383.x","volume":"57","author":"J Ibrahim","year":"2001","unstructured":"Ibrahim J, Chen M-H, Sinha D (2001) Bayesian semi-parametric models for survival data with a cure fraction. Biometrics 57:383\u2013388","journal-title":"Biometrics"},{"issue":"3","key":"9729_CR19","doi-asserted-by":"publisher","first-page":"576","DOI":"10.1093\/biostatistics\/kxl030","volume":"8","author":"PC Lambert","year":"2007","unstructured":"Lambert PC, Thompson JR, Weston CL, Dickman PW (2007) Estimating and modeling the cure fraction in population-based cancer survival analysis. Biostatistics 8(3):576\u2013594","journal-title":"Biostatistics"},{"key":"9729_CR20","doi-asserted-by":"publisher","first-page":"3235","DOI":"10.1002\/sim.1260","volume":"21","author":"C-S Li","year":"2002","unstructured":"Li C-S, Taylor JM (2002) A semi-parametric accelerated failure time cure model. Stat Med 21:3235\u20133247","journal-title":"Stat Med"},{"issue":"4","key":"9729_CR21","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1016\/S0167-7152(01)00105-5","volume":"54","author":"C-S Li","year":"2001","unstructured":"Li C-S, Taylor JM, Sy JP (2001) Identifiability of cure models. Stat Probab Lett 54(4):389\u2013395","journal-title":"Stat Probab Lett"},{"key":"9729_CR22","volume-title":"Survival analysis with longterm survivors","author":"RA Maller","year":"1996","unstructured":"Maller RA, Zhou X (1996) Survival analysis with longterm survivors. Wiley, Chichester"},{"issue":"7","key":"9729_CR23","doi-asserted-by":"publisher","first-page":"589","DOI":"10.1056\/NEJMoa2304194","volume":"389","author":"IK Mellinghoff","year":"2023","unstructured":"Mellinghoff IK, Van Den Bent MJ, Blumenthal DT, Touat M, Peters KB, Clarke J, Mendez J, Yust-Katz S, Welsh L, Mason WP et al (2023) Vorasidenib in IDH1-or IDH2-mutant low-grade glioma. N Engl J Med 389(7):589\u2013601","journal-title":"N Engl J Med"},{"key":"9729_CR24","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10985-018-9417-8","volume":"25","author":"MA Nicolaie","year":"2019","unstructured":"Nicolaie MA, Taylor JMG, Legrand C (2019) Vertical modeling: analysis of competing risks data with a cure fraction. Lifetime Data Anal 25:1\u201325","journal-title":"Lifetime Data Anal"},{"key":"9729_CR25","unstructured":"Peng Y, Taylor JM (2014) Cure models. In: Handbook of survival analysis, vol 34. CRC Press, pp 113\u2013134"},{"key":"9729_CR26","volume-title":"Cure models: methods, applications, and implementation","author":"Y Peng","year":"1996","unstructured":"Peng Y, Yu B (1996) Cure models: methods, applications, and implementation. Chapman and Hall\/CRC, Boca Raton"},{"key":"9729_CR27","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1002\/sim.4780010202","volume":"1","author":"SJ Pocock","year":"1982","unstructured":"Pocock SJ, Gore SM, Kerr GR (1982) Long-term survival analysis: the curability of breast cancer. Stat Med 1:93\u2013104","journal-title":"Stat Med"},{"key":"9729_CR28","volume-title":"Dynamic prediction in clinical survival analysis","author":"HC van Houwelingen","year":"2012","unstructured":"van Houwelingen HC, Putter H (2012) Dynamic prediction in clinical survival analysis. Chapman and Hall\/CRC, Boca Raton"},{"key":"9729_CR29","unstructured":"Wang W, Chen K, Yan J (2021) intsurv: integrative survival models. R package version 0.2.2"},{"key":"9729_CR30","doi-asserted-by":"publisher","first-page":"1486","DOI":"10.1056\/NEJMoa2403614","volume":"391","author":"J Xi","year":"2024","unstructured":"Xi J, Henry D (2024) Amivantamab plus lazertinib for previously untreated EGFR-mutated advanced NSCLC. N Engl J Med 391:1486\u20131498","journal-title":"N Engl J Med"},{"issue":"10","key":"9729_CR31","doi-asserted-by":"publisher","first-page":"1976","DOI":"10.1177\/09622802221106300","volume":"31","author":"X Xue","year":"2022","unstructured":"Xue X, Saeed O, Castagna F, Jorde U, Agalliu I (2022) The analysis of COVID-19 in-hospital mortality: a competing risk approach or a cure model? Stat Methods Med Res 31(10):1976\u20131991","journal-title":"Stat Methods Med Res"},{"key":"9729_CR32","doi-asserted-by":"publisher","DOI":"10.1142\/2420","volume-title":"Stochastic models of tumor latency and their biostatistical applications","author":"AY Yakovlev","year":"1996","unstructured":"Yakovlev AY, Tsodikov AD, Asselain B (1996) Stochastic models of tumor latency and their biostatistical applications. World Scientific, Singapore"},{"issue":"11","key":"9729_CR33","doi-asserted-by":"publisher","first-page":"1733","DOI":"10.1002\/sim.1774","volume":"23","author":"B Yu","year":"2004","unstructured":"Yu B, Tiwari RC, Cronin KA, Feuer EJ (2004) Cure fraction estimation from the mixture cure models for grouped survival data. Stat Med 23(11):1733\u20131747","journal-title":"Stat Med"}],"container-title":["Lifetime Data Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10985-026-09729-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10985-026-09729-7","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10985-026-09729-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,10]],"date-time":"2026-09-10T15:57:13Z","timestamp":1789055833000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10985-026-09729-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,10]]},"references-count":33,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2026,12]]}},"alternative-id":["9729"],"URL":"https:\/\/doi.org\/10.1007\/s10985-026-09729-7","relation":{},"ISSN":["1380-7870","1572-9249"],"issn-type":[{"value":"1380-7870","type":"print"},{"value":"1572-9249","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,10]]},"assertion":[{"value":"28 January 2026","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 August 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 September 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"51"}}