Illness-death model: statistical perspective and differential equations

Ralph Brinks () and Annika Hoyer ()
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Ralph Brinks: University Hospital Duesseldorf
Annika Hoyer: German Diabetes Center

Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, 2018, vol. 24, issue 4, No 14, 743-754

Abstract: Abstract The aim of this work is to relate the theory of stochastic processes with the differential equations associated with multistate (compartment) models. We show that the Kolmogorov Forward Differential Equations can be used to derive a relation between the prevalence and the transition rates in the illness-death model. Then, we prove mathematical well-definedness and epidemiological meaningfulness of the prevalence of the disease. As an application, we derive the incidence of diabetes from a series of cross-sections.

Keywords: Fix-Neyman competing risks model; Illness-death model; Multistate models; Non-parametric estimation of transition rates; Incidence; Prevalence; Markov processes; Kolmogorov Differential Equations (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10985-018-9419-6

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