Maximum likelihood estimation for aggregate current status data: Simulation study using the illness-death model for chronic diseases with duration dependency

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.