  This note considers the problem of conducting statistical inference on the
share of individuals in some subgroup of a population that experience some
event. The specific complication is that the size of the subgroup needs to be
estimated, whereas the number of individuals that experience the event is
known. The problem is motivated by the recent study of Streeck et al. (2020),
who estimate the infection fatality rate (IFR) of SARS-CoV-2 infection in a
German town that experienced a super-spreading event in mid-February 2020. In
their case the subgroup of interest is comprised of all infected individuals,
and the event is death caused by the infection. We clarify issues with the
precise definition of the target parameter in this context, and propose
confidence intervals (CIs) based on classical statistical principles that
result in good coverage properties.
