  We use the illness-death model (IDM) for chronic conditions to derive a new
analytical relation between the transition rates between the states of the IDM.
The transition rates are the incidence rate (i) and the mortality rates of
people without disease (m0) and with disease (m1). For the most generic case,
the rates depend on age, calendar time and in case of m1 also on the duration
of the disease. In this work, we show that the prevalence-odds can be expressed
as a convolution-like product of the incidence rate and an exponentiated linear
combination of i, m0 and m1. The analytical expression can be used as the basis
for a maximum likelihood estimation (MLE) and associated large sample
asymptotics. In a simulation study where a cross-sectional trial about a
chronic condition is mimicked, we estimate the duration dependency of the
mortality rate m1 based on aggregated current status data using the ML
estimator. For this, the number of study participants and the number of
diseased people in eleven age groups are considered. The ML estimator provides
reasonable estimates for the parameters including their large sample confidence
bounds.
