Estimation of the transition rates in the illness-death model for chronic diseases from aggregated current status data: a feasibility and simulation study

Recently, it has been shown that the transition rates of the illness-death model (IDM) for chronic conditions are related to the age-specific prevalence by a partial differential equation (PDE). Given mortality, the PDE could be used to estimate incidence rates from cross-sectional data. The aim of this article is to extend the IDM and introduce a novel method to estimate the age-specific incidence rate together with the two mortality rates from aggregated current status (ACS) data. By ACS data we mean counts of people in the four states of the extended IDM at different points in time. ACS data stem from epidemiological studies where only current disease status and vital status data need to be collected without following-up people (as, for example, in cohort studies). To demonstrate feasibility of the method, we use a simulation study from the context of diabetes in Germany. Two estimation methods are introduced, a least squares estimator and a maximum likelihood estimator. We find a good agreement between the estimates and the input parameters used to set up the simulation.