Estimation of incidence from aggregated current status data without differential mortality

We use a historical data about breathlessness in British coal miners to compare two methods centered around a differential equation for deriving the age-specific incidence from aggregated current status data with age information, i.e. age-specific prevalence data. Special focus is put on estimating confidence bounds. For this, we derive a maximum likelihood (ML) estimator for estimating the age-specific incidence from the prevalence data and confidence bounds are calculated based on classical ML theory. Second, we construct a Markov-Chain-Monte-Carlo (MCMC) algorithm to estimate confidence bounds, which implements a weighted version of the differential equation into the prior of the MCMC algorithm. The confidence bounds for both methods are compared and it turns out that the MCMC estimates approach the ML estimates if the prior gives strong weight to the differential equation.