  With the beginning of the COVID-19 pandemic, we became aware of the need for
comprehensive data collection and its provision to scientists and experts for
proper data analyses. In Germany, the Robert Koch Institute (RKI) has tried to
keep up with this demand for data on COVID-19, but there were (and still are)
relevant data missing that are needed to understand the whole picture of the
pandemic. In this paper, we take a closer look at the severity of the course of
COVID-19 in Germany, for which ideal information would be the number of
incoming patients to ICU units. This information was (and still is) not
available. Instead, the current occupancy of ICU units on the district level
was reported daily. We demonstrate how this information can be used to predict
the number of incoming as well as released COVID-19 patients using a stochastic
version of the Expectation Maximisation algorithm (SEM). This in turn, allows
for estimating the influence of district-specific and age-specific infection
rates as well as further covariates, including spatial effects, on the number
of incoming patients. The paper demonstrates that even if relevant data are not
recorded or provided officially, statistical modelling allows for
reconstructing them. This also includes the quantification of uncertainty which
naturally results from the application of the SEM algorithm.
