title: Limits of applicability for the deterministic approximation of the two-step clonal expansion model.
abstract: Motivated by a hypothesis published recently, the limits of applicability of the deterministic approximation of the two-step clonal expansion model are investigated. The approximate hazard increases unlimited, while the exact hazard is approaching a constant value. The approximate solution becomes inapplicable for hazards in the order of that constant rate. When the initiation rate is much larger than the cell division rate, the survival rate is small when the approximation becomes inapplicable. The simplicity of the exact solutions suggests using them in all situations.
authors.affiliation: GSF, Institute of Radiation Protection, Neuherberg, Germany. heidenreich@gsf.de
authors.forename: W F
authors.initials: WF
authors.lastname: Heidenreich
authors.forename: R
authors.initials: R
authors.lastname: Hoogenveen
mesh_terms: D003043:Cocarcinogenesis; D006801:Humans; D008954:Models, Biological; D009154:Mutation; D009369:Neoplasms / Q000209:etiology / Q000235:genetics / Q000473:pathology; D011336:Probability; D016016:Proportional Hazards Models; D018570:Risk Assessment / Q000706:statistics & numerical data*; D016019:Survival Analysis