{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,31]],"date-time":"2026-08-31T14:02:06Z","timestamp":1788184926906,"version":"build-2803163510"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,1,24]],"date-time":"2026-01-24T00:00:00Z","timestamp":1769212800000},"content-version":"vor","delay-in-days":23,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Eur J Epidemiol"],"published-print":{"date-parts":[[2026,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Amyotrophic lateral sclerosis (ALS) is a multifactorial neurodegenerative disease whose incidence increases with age. According to the gene\u2013time\u2013environment hypothesis, ALS onset occurs through the interaction between genes and environmental exposures during ageing, which may involve a continuous accumulation process. Alternatively, the multistep pathogenic hypothesis, based on the Armitage-Doll multistep model from cancer research, posits that a discrete number of specific sequential \u201chits\u201d are necessary to trigger ALS. Here we analyzed three large population-based epidemiological datasets of ALS to formally test whether the ALS age-incidence curve is better described by a power law, as predicted by the Armitage-Doll model, or by an exponential function, which is generally associated to continuous accumulation of damage and is incompatible with the Armitage-Doll model. We obtained moderate-to-extreme Bayesian evidence in favor of the exponential function compared to the power law. Cancer data were instead better aligned, as expected, with the power law. These results suggest that the multistep pathogenesis hypothesis based on the Armitage-Doll model cannot be extended from cancer to ALS, because it is incompatible with the epidemiological data. This calls for a re-consideration of the current understanding of ALS pathogenesis. Our work also warns against extending the Armitage-Doll multistep model from cancer to other aging-related diseases solely based on age-incidence curves.<\/jats:p>","DOI":"10.1007\/s10654-025-01289-8","type":"journal-article","created":{"date-parts":[[2026,1,24]],"date-time":"2026-01-24T07:14:54Z","timestamp":1769238894000},"page":"1-13","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["The multistep pathogenic hypothesis of amyotrophic lateral sclerosis is incompatible with the epidemiological data"],"prefix":"10.1007","volume":"41","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7289-6668","authenticated-orcid":false,"given":"Guglielmo","family":"Foffani","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Daniele","family":"Urso","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Josh","family":"Hiller","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marco","family":"Piccininni","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Beno\u00eet","family":"Marin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Giancarlo","family":"Logroscino","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,1,24]]},"reference":[{"key":"1289_CR1","doi-asserted-by":"publisher","first-page":"17071","DOI":"10.1038\/nrdp.2017.71","volume":"3","author":"O Hardiman","year":"2017","unstructured":"Hardiman O, Al-Chalabi A, Chio A, Corr EM, Logroscino G, Robberecht W, et al. Amyotrophic lateral sclerosis. Nat Rev Dis Prim. 2017;3:17071.","journal-title":"Nat Rev Dis Prim"},{"key":"1289_CR2","doi-asserted-by":"publisher","first-page":"621","DOI":"10.1007\/s10654-018-0392-x","volume":"33","author":"B Marin","year":"2018","unstructured":"Marin B, Fontana A, Arcuti S, Copetti M, Boum\u00e9diene F, Couratier P, et al. Age-specific ALS incidence: a dose\u2013response meta-analysis. Eur J Epidemiol. 2018;33:621\u201334. https:\/\/doi.org\/10.1007\/s10654-018-0392-x.","journal-title":"Eur J Epidemiol"},{"key":"1289_CR3","doi-asserted-by":"publisher","first-page":"617","DOI":"10.1038\/nrneurol.2013.203","volume":"9","author":"A Al-Chalabi","year":"2013","unstructured":"Al-Chalabi A, Hardiman O. The epidemiology of ALS: a conspiracy of genes, environment and time. Nat Rev Neurol. 2013;9:617\u201328.","journal-title":"Nat Rev Neurol"},{"key":"1289_CR4","doi-asserted-by":"publisher","first-page":"465","DOI":"10.1016\/S1474-4422(21)00414-2","volume":"21","author":"SA Goutman","year":"2022","unstructured":"Goutman SA, Hardiman O, Al-Chalabi A, Chi\u00f3 A, Savelieff MG, Kiernan MC, et al. Emerging insights into the complex genetics and pathophysiology of amyotrophic lateral sclerosis. Lancet Neurol. 2022;21:465\u201379.","journal-title":"Lancet Neurol"},{"key":"1289_CR5","doi-asserted-by":"publisher","first-page":"1108","DOI":"10.1016\/S1474-4422(14)70219-4","volume":"13","author":"A Al-Chalabi","year":"2014","unstructured":"Al-Chalabi A, Calvo A, Chio A, Colville S, Ellis CM, Hardiman O, et al. Analysis of amyotrophic lateral sclerosis as a multistep process: a population-based modelling study. Lancet Neurol. 2014;13:1108\u201313.","journal-title":"Lancet Neurol"},{"key":"1289_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/bjc.1954.1","volume":"8","author":"P Armitage","year":"1954","unstructured":"Armitage P, Doll R. The age distribution of cancer and a multi-stage theory of carcinogenesis. Br J Cancer. 1954;8:1\u201312.","journal-title":"Br J Cancer"},{"key":"1289_CR7","doi-asserted-by":"publisher","first-page":"e635","DOI":"10.1212\/WNL.0000000000005996","volume":"91","author":"A Chi\u00f2","year":"2018","unstructured":"Chi\u00f2 A, Mazzini L, D\u2019Alfonso S, Corrado L, Canosa A, Moglia C, et al. The multistep hypothesis of ALS revisited: the role of genetic mutations. Neurology. 2018;91:e635-42.","journal-title":"Neurology."},{"key":"1289_CR8","doi-asserted-by":"publisher","first-page":"e1657","DOI":"10.1212\/WNL.0000000000009015","volume":"94","author":"S Vucic","year":"2020","unstructured":"Vucic S, Higashihara M, Sobue G, Atsuta N, Doi Y, Kuwabara S, et al. ALS is a multistep process in South Korean, Japanese, and Australian patients. Neurology. 2020;94:e1657-63.","journal-title":"Neurology"},{"key":"1289_CR9","doi-asserted-by":"publisher","first-page":"532","DOI":"10.1080\/21678421.2018.1556697","volume":"20","author":"S Vucic","year":"2019","unstructured":"Vucic S, Westeneng H-J, Al-Chalabi A, Van Den Berg LH, Talman P, Kiernan MC. Amyotrophic lateral sclerosis as a multi-step process: an Australia population study. Amyotroph Lateral Scler Frontotemporal Degener. 2019;20:532\u20137. https:\/\/doi.org\/10.1080\/21678421.2018.1556697.","journal-title":"Amyotroph Lateral Scler Frontotemporal Degener"},{"key":"1289_CR10","doi-asserted-by":"publisher","DOI":"10.1080\/21678421.2022.2035765","author":"SJ Choi","year":"2022","unstructured":"Choi SJ, Park CHK, Hong YH, Sung JJ. Previous psychiatric disorders in the multistep hypothesis of amyotrophic lateral sclerosis: a South Korean population study. Amyotroph Lateral Scler Frontotemporal Degener. 2022. https:\/\/doi.org\/10.1080\/21678421.2022.2035765.","journal-title":"Amyotroph Lateral Scler Frontotemporal Degener"},{"key":"1289_CR11","doi-asserted-by":"publisher","first-page":"421","DOI":"10.1111\/ene.14554","volume":"28","author":"FC Garton","year":"2021","unstructured":"Garton FC, Trabjerg BB, Wray NR, Agerbo E. Cardiovascular disease, psychiatric diagnosis and sex differences in the multistep hypothesis of amyotrophic lateral sclerosis. Eur J Neurol. 2021;28:421\u20139. https:\/\/doi.org\/10.1111\/ene.14554.","journal-title":"Eur J Neurol"},{"key":"1289_CR12","doi-asserted-by":"publisher","first-page":"1363","DOI":"10.1016\/S0140-6736(22)01272-7","volume":"400","author":"EL Feldman","year":"2022","unstructured":"Feldman EL, Goutman SA, Petri S, Mazzini L, Savelieff MG, Shaw PJ, et al. Amyotrophic lateral sclerosis. Lancet. 2022;400:1363\u201380.","journal-title":"Lancet"},{"key":"1289_CR13","doi-asserted-by":"publisher","first-page":"617","DOI":"10.1038\/s41582-023-00867-2","volume":"19","author":"SA Goutman","year":"2023","unstructured":"Goutman SA, Savelieff MG, Jang D-G, Hur J, Feldman EL. The amyotrophic lateral sclerosis exposome: recent advances and future directions. Nat Rev Neurol. 2023;19:617\u201334.","journal-title":"Nat Rev Neurol"},{"key":"1289_CR14","doi-asserted-by":"publisher","first-page":"1163","DOI":"10.18632\/aging.101816","volume":"11","author":"S Licher","year":"2019","unstructured":"Licher S, van der Willik KD, Vinke EJ, Yilmaz P, Fani L, Schagen SB, et al. Alzheimer\u2019s disease as a multistage process: an analysis from a population-based cohort study. Aging (Albany NY). 2019;11:1163\u201376. https:\/\/doi.org\/10.18632\/aging.101816.","journal-title":"Aging (Albany NY)"},{"key":"1289_CR15","doi-asserted-by":"publisher","first-page":"18923","DOI":"10.1038\/s41598-020-75014-8","volume":"10","author":"D Gerovska","year":"2020","unstructured":"Gerovska D, Irizar H, Otaegi D, Ferrer I, L\u00f3pez de Munain A, Ara\u00fazo-Bravo MJ. Genealogy of the neurodegenerative diseases based on a meta-analysis of age-stratified incidence data. Sci Rep. 2020;10:18923.","journal-title":"Sci Rep"},{"key":"1289_CR16","doi-asserted-by":"publisher","first-page":"2530","DOI":"10.1002\/mds.28719","volume":"36","author":"C Le Heron","year":"2021","unstructured":"Le Heron C, MacAskill M, Mason D, Dalrymple-Alford J, Anderson T, Pitcher T, et al. A multi-step model of Parkinson\u2019s disease pathogenesis. Mov Disord. 2021;36:2530\u20138.","journal-title":"Mov Disord"},{"key":"1289_CR17","doi-asserted-by":"publisher","DOI":"10.1186\/s13578-021-00737-8","author":"D Gerovska","year":"2022","unstructured":"Gerovska D, Ara\u00fazo-Bravo MJ. The common incidence-age multistep model of neurodegenerative diseases revisited: wider general age range of incidence corresponds to fewer disease steps. Cell Biosci. 2022. https:\/\/doi.org\/10.1186\/s13578-021-00737-8.","journal-title":"Cell Biosci"},{"key":"1289_CR18","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10654-020-00711-7","volume":"36","author":"N Pearce","year":"2021","unstructured":"Pearce N, Moirano G, Maule M, Kogevinas M, Rodo X, Lawlor DA, et al. Does death from Covid-19 arise from a multi-step process? Eur J Epidemiol. 2021;36:1\u20139. https:\/\/doi.org\/10.1007\/s10654-020-00711-7.","journal-title":"Eur J Epidemiol"},{"key":"1289_CR19","first-page":"7","volume":"8","author":"WZ Billings","year":"2022","unstructured":"Billings WZ, Clifton J, Hiller J, Meek T, Penland A, Rogers W, et al. An axiomatic and contextual review of the armitage and doll model of carcinogenesis. SPORA A J Biomath. 2022;8:7\u201315.","journal-title":"SPORA A J Biomath"},{"key":"1289_CR20","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1115\/1.4010337","volume":"18","author":"W Weibull","year":"1951","unstructured":"Weibull W. A statistical distribution function of wide applicability. J Appl Mech. 1951;18:293\u20137.","journal-title":"J Appl Mech"},{"key":"1289_CR21","doi-asserted-by":"publisher","first-page":"20140379","DOI":"10.1098\/rstb.2014.0379","volume":"370","author":"TBL Kirkwood","year":"2015","unstructured":"Kirkwood TBL. Deciphering death: a commentary on Gompertz (1825) \u2018on the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies.\u2019 Philos Trans R Soc Lond B Biol Sci. 2015;370:20140379.","journal-title":"Philos Trans R Soc Lond B Biol Sci"},{"key":"1289_CR22","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1016\/j.cell.2005.01.027","volume":"120","author":"TBL Kirkwood","year":"2005","unstructured":"Kirkwood TBL. Understanding the odd science of aging. Cell. 2005;120:437\u201347.","journal-title":"Cell"},{"key":"1289_CR23","doi-asserted-by":"publisher","first-page":"1941","DOI":"10.1098\/rspb.2005.3192","volume":"272","author":"DB Fonseca","year":"2005","unstructured":"Fonseca DB, Brancato CL, Prior AE, Shelton PMJ, Sheehy MRJ. Death rates reflect accumulating brain damage in arthropods. Proc Biol Sci. 2005;272:1941\u20138. https:\/\/doi.org\/10.1098\/rspb.2005.3192.","journal-title":"Proc Biol Sci"},{"key":"1289_CR24","doi-asserted-by":"publisher","first-page":"e0233384","DOI":"10.1371\/journal.pone.0233384","volume":"15","author":"A Ledberg","year":"2020","unstructured":"Ledberg A. Exponential increase in mortality with age is a generic property of a simple model system of damage accumulation and death. PLoS ONE. 2020;15:e0233384.","journal-title":"PLoS ONE"},{"key":"1289_CR25","doi-asserted-by":"publisher","first-page":"e13314","DOI":"10.1111\/acel.13314","volume":"20","author":"I Katzir","year":"2021","unstructured":"Katzir I, Adler M, Karin O, Mendelsohn-Cohen N, Mayo A, Alon U. Senescent cells and the incidence of age-related diseases. Aging Cell. 2021;20:e13314.","journal-title":"Aging Cell"},{"key":"1289_CR26","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1289\/ehp.8563195","volume":"63","author":"P Armitage","year":"1985","unstructured":"Armitage P. Multistage models of carcinogenesis. Environ Health Perspect. 1985;63:195\u2013201.","journal-title":"Environ Health Perspect"},{"key":"1289_CR27","doi-asserted-by":"publisher","first-page":"1983","DOI":"10.1038\/sj.bjc.6602297","volume":"91","author":"P Armitage","year":"2004","unstructured":"Armitage P, Doll R. The age distribution of cancer and a multi-stage theory of carcinogenesis. Br J Cancer. 2004;91:1983\u20139.","journal-title":"Br J Cancer"},{"key":"1289_CR28","doi-asserted-by":"publisher","DOI":"10.2307\/2986270","author":"P Royston","year":"1994","unstructured":"Royston P, Altman DG. Regression using fractional polynomials of continuous covariates: parsimonious parametric modelling. Appl Stat. 1994. https:\/\/doi.org\/10.2307\/2986270.","journal-title":"Appl Stat"},{"key":"1289_CR29","doi-asserted-by":"publisher","first-page":"916","DOI":"10.1002\/1097-0142(195109)4:5<916::AID-CNCR2820040504>3.0.CO;2-7","volume":"4","author":"JC Fisher","year":"1951","unstructured":"Fisher JC, Hollomon JH. A hypothesis for the origin of cancer foci. Cancer. 1951;4:916\u20138.","journal-title":"Cancer"},{"key":"1289_CR30","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1038\/bjc.1953.8","volume":"7","author":"CO Nordling","year":"1953","unstructured":"Nordling CO. A new theory on the cancer-inducing mechanism. Br J Cancer. 1953;7:68\u201372.","journal-title":"Br J Cancer"},{"key":"1289_CR31","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1038\/35101031","volume":"1","author":"AG Knudson","year":"2001","unstructured":"Knudson AG. Two genetic hits (more or less) to cancer. Nat Rev Cancer. 2001;1:157\u201362.","journal-title":"Nat Rev Cancer"},{"key":"1289_CR32","doi-asserted-by":"publisher","first-page":"1546","DOI":"10.1126\/science.1235122","volume":"339","author":"B Vogelstein","year":"2013","unstructured":"Vogelstein B, Papadopoulos N, Velculescu VE, Zhou S, Diaz LA, Kinzler KW. Cancer genome landscapes. Science. 2013;339:1546\u201358.","journal-title":"Science"},{"key":"1289_CR33","doi-asserted-by":"publisher","first-page":"12157","DOI":"10.1038\/ncomms12157","volume":"7","author":"DI Podolskiy","year":"2016","unstructured":"Podolskiy DI, Lobanov AV, Kryukov GV, Gladyshev VN. Analysis of cancer genomes reveals basic features of human aging and its role in cancer development. Nat Commun. 2016;7:12157.","journal-title":"Nat Commun"},{"key":"1289_CR34","doi-asserted-by":"publisher","first-page":"1883","DOI":"10.1073\/pnas.1714478115","volume":"115","author":"S Palmer","year":"2018","unstructured":"Palmer S, Albergante L, Blackburn CC, Newman TJ. Thymic involution and rising disease incidence with age. Proc Natl Acad Sci U S A. 2018;115:1883\u20138. https:\/\/doi.org\/10.1073\/pnas.1714478115.","journal-title":"Proc Natl Acad Sci U S A"},{"key":"1289_CR35","doi-asserted-by":"publisher","first-page":"1105","DOI":"10.1002\/mds.28997","volume":"37","author":"G Foffani","year":"2022","unstructured":"Foffani G. An exponential rather than multistep model of Parkinson\u2019s disease pathogenesis. Mov Disord. 2022;37:1105\u20136. https:\/\/doi.org\/10.1002\/mds.28997.","journal-title":"Mov Disord"},{"key":"1289_CR36","doi-asserted-by":"publisher","first-page":"1083","DOI":"10.1016\/S1474-4422(18)30404-6","volume":"17","author":"G Logroscino","year":"2018","unstructured":"Logroscino G, Piccininni M, Marin B, Nichols E, Abd-Allah F, Abdelalim A, et al. Global, regional, and national burden of motor neuron diseases 1990\u20132016: a systematic analysis for the global burden of disease study 2016. Lancet Neurol. 2018;17:1083\u201397.","journal-title":"Lancet Neurol"},{"key":"1289_CR37","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1191\/0748233703th195oa","volume":"19","author":"G Ritter","year":"2003","unstructured":"Ritter G, Wilson R, Pompei F, Burmistrov D. The multistage model of cancer development: some implications. Toxicol Ind Health. 2003;19:125\u201345.","journal-title":"Toxicol Ind Health"}],"container-title":["European Journal of Epidemiology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10654-025-01289-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10654-025-01289-8","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10654-025-01289-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,6]],"date-time":"2026-02-06T05:05:47Z","timestamp":1770354347000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10654-025-01289-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1]]},"references-count":37,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,1]]}},"alternative-id":["1289"],"URL":"https:\/\/doi.org\/10.1007\/s10654-025-01289-8","relation":{},"ISSN":["0393-2990","1573-7284"],"issn-type":[{"value":"0393-2990","type":"print"},{"value":"1573-7284","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1]]},"assertion":[{"value":"26 November 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 July 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 January 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no conflicts of interest related to the present study.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"The present study is a re-analysis of previously published epidemiological data, so no ethical approval is required.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}}]}}