On Keiding's Equation and its relation to differential equations about prevalence and incidence in chronic disease epidemiology

TL;DR

This paper explores the mathematical relationship between prevalence, incidence, and mortality in chronic disease models, extending Keiding's equation and proposing a simplified incidence estimate from prevalence data.

Contribution

It demonstrates that Keiding's equation generalizes previous PDE solutions and introduces a simple incidence estimation method in specific cases.

Findings

Keiding's equation generalizes Brunet and Struchiner's PDE solution.

A simple incidence estimate from prevalence data is proposed.

The model considers multiple time scales: age, calendar time, and disease duration.

Abstract

We study the relation between the age-specific prevalence, incidence and mortality in an illness-death model consisting of the three states Healthy, Ill, Dead. The dependency on three different time scales (age, calendar time, disease duration) is considered. It is shown that Keiding's equation published in 1991 is a generalisation of the solution of Brunet and Struchiner's partial differential equation from 1999. In a special case, we propose a particularly simple estimate of the incidence from prevalence data.