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Math. Biol."],"published-print":{"date-parts":[[2026,6]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>We present a new approach for jointly modelling the natural history of ductal carcinoma in situ (DCIS) and invasive breast cancer, based on a continuous tumor growth framework. We first describe the structure of a stable disease population, in which individuals traverse with rates invariant to calendar time through different health states. Based on the properties of this population we develop a likelihood model that jointly utilizes probability distributions describing sub-models for screening sensitivity, detection through symptoms, tumor growth rate and time for DCIS to become invasive. This model can incorporate any parametric forms for these sub-models, allowing for testing different assumptions for the occult biological progression of breast cancer. By using stable disease assumptions the model can be fitted to data from incident cancer cases and does not require specification of a sub-model for age at tumour onset. In the final part of the publication we perform simulations to verify the theoretical properties of the stable disease population and to show how our model can be used in a real setting to estimate characteristics of the involved latent processes.<\/jats:p>","DOI":"10.1007\/s00285-026-02418-x","type":"journal-article","created":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T19:01:04Z","timestamp":1780426864000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A framework for jointly modeling the natural history of ductal carcinoma in situ and invasive breast cancer"],"prefix":"10.1007","volume":"92","author":[{"given":"Evripidis","family":"Kapanidis","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Keith","family":"Humphreys","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,6,2]]},"reference":[{"issue":"4","key":"2418_CR1","doi-asserted-by":"publisher","first-page":"1620","DOI":"10.1177\/0962280213492843","volume":"25","author":"L Abrahamsson","year":"2016","unstructured":"Abrahamsson L, Humphreys K (2016) A statistical model of breast cancer tumour growth with estimation of screening sensitivity as a function of mammographic density. 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