Abstract
BackgroundRecently, we have shown that the age-specific prevalence of a disease can be related to the transition rates in the illness-death model via a partial differential equation (PDE). The transition rates are the incidence rate, the remission rate and mortality rates from the ‘Healthy’ and ‘Ill’ states. In case of a chronic disease, we now demonstrate that the PDE can be used to estimate the excess mortality from age-specific prevalence and incidence data. For the prevalence and incidence, aggregated data are sufficient - no individual subject data are needed, which allows application of the methods in contexts of strong data protection or where data from individual subjects is not accessible.MethodsAfter developing novel estimators for the excess mortality derived from the PDE, we apply them to simulated data and compare the findings with the input values of the simulation aiming to evaluate the new approach. In a practical application to claims data from 35 million men insured by the German public health insurance funds, we estimate the population-wide excess mortality of men with diagnosed type 2 diabetes.ResultsIn the simulation study, we find that the estimation of the excess mortality is feasible from prevalence and incidence data if the prevalence is given at two points in time. The accuracy of the method decreases as the temporal difference between these two points in time increases. In our setting, the relative error was 5% and below if the temporal difference was three years or less. Application of the new method to the claims data yields plausible findings for the excess mortality of type 2 diabetes in German men.ConclusionsThe described approach is useful to estimate the excess mortality of a chronic condition from aggregated age-specific incidence and prevalence data.Trial registrationThe article does not report the results of any health care intervention.
Highlights
Recently, we have shown that the age-specific prevalence of a health state or disease can be related to the transition rates in the illness-death model via a partial differential equation (PDE) [1, 2]
We demonstrate that it is possible to estimate excess mortality from age-specific prevalence and incidence of a chronic disease
Illness-death model The age-specific prevalence p(t, a) = I(t, a)/{H(t, a) + I(t, a)} i.e., the percentage of people aged a at time t who are chronically ill, is the solution of the following partial differential equation (PDE): ð∂t þ ∂aÞp 1⁄4 ð1−pÞfi−pðm1−m0Þg ð3Þ
Summary
We have shown that the age-specific prevalence of a disease can be related to the transition rates in the illness-death model via a partial differential equation (PDE). We have shown that the age-specific prevalence of a health state or disease can be related to the transition rates in the illness-death model via a partial differential equation (PDE) [1, 2]. The mortality rate ratio R expresses the mortality rate of the diseased people relative to the non-diseased at the same age Due to this plain interpretation, R is more often used than the (absolute) excess mortality Δm.
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