title: Deriving age-specific incidence from prevalence with an ordinary differential equation.
abstract: This article describes new relationships between the age-specific incidence of, the prevalence of and mortality from a chronic disease. We express these relationships in terms of an ordinary differential equation and form the methodological basis for a novel approach to estimating incidences from age-specific prevalence data. We examine practical aspects of the relationships and a comparison with a known stochastic method in a simulation study. Finally, we apply the novel method to a data set of renal replacement therapy recorded from patients with chronic kidney failure in a region of Germany with approximately 310,000 inhabitants from 2002 to 2010.
authors.affiliation: Institute for Biometry and Epidemiology, German Diabetes Centre, Duesseldorf, Germany. ralph.brinks@ddz.uni-duesseldorf.de
authors.forename: Ralph
authors.initials: R
authors.lastname: Brinks
authors.forename: Sandra
authors.initials: S
authors.lastname: Landwehr
authors.forename: Andrea
authors.initials: A
authors.lastname: Icks
authors.forename: Michael
authors.initials: M
authors.lastname: Koch
authors.forename: Guido
authors.initials: G
authors.lastname: Giani
mesh_terms: D000328:Adult; D000368:Aged; D002908:Chronic Disease / Q000453:epidemiology* / Q000401:mortality; D003198:Computer Simulation; D003430:Cross-Sectional Studies; D003627:Data Interpretation, Statistical; D004812:Epidemiologic Methods; D005858:Germany / Q000453:epidemiology; D006801:Humans; D015994:Incidence; D007676:Kidney Failure, Chronic / Q000453:epidemiology / Q000401:mortality; D008875:Middle Aged; D015995:Prevalence