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. 2015 Dec;32(4):425-35.
doi: 10.1093/imammb/dqu024. Epub 2015 Jan 9.

A new relation between prevalence and incidence of a chronic disease

Ralph Brinks  1 , Sandra Landwehr  2
Affiliations

A new relation between prevalence and incidence of a chronic disease

Ralph Brinks et al. Math Med Biol. 2015 Dec.

Abstract

In 1991 Keiding published a relation between the age-specific prevalence and incidence of a chronic disease (in Age-specific incidence and prevalence: a statistical perspective. J. Roy. Stat. Soc. A, 154, 371-412). For special cases alternative formulations by differential equations were given recently in Brinks et al. (2013, Deriving age-specific incidence from prevalence with an ordinary differential equation. Statist. Med., 32, 2070-2078) and in Brinks & Landwehr (2014, Age- and time-dependent model of the prevalence of non-communicable diseases and application to dementia in Germany, Theor. Popul. Biol., 92, 62-68). From these works, we generalize formulations and discuss the advantages of the novel approach. As an implication, we obtain a new way of estimating the incidence rate of a chronic disease from prevalence data. This enables us to employ cross-sectional studies where otherwise expensive and lengthy follow-up studies are needed. This article illustrates and validates the novel method in a simulation study about dementia in Germany.

Keywords: chronic diseases; compartment models; dementia; incidence; mortality; prevalence.

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Figures

Fig. 1.
Fig. 1.
Compartment model with three states and transition rates depending on different time scales: calendar time formula image age formula image and duration formula image
Fig. 2.
Fig. 2.
Age-specific prevalence in 2010 and 2015 (example without duration dependency).
See this image and copyright information in PMC

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