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This note considers the problem of conducting statistical inference on theshare of individuals in some subgroup of a population that experience someevent. The specific complication is that the size of the subgroup needs to beestimated, whereas the number of individuals that experience the event isknown. 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 aGerman town that experienced a super-spreading event in mid-February 2020. Intheir case the subgroup of interest is comprised of all infected individuals,and the event is death caused by the infection. We clarify issues with theprecise definition of the target parameter in this context, and proposeconfidence intervals (CIs) based on classical statistical principles thatresult in good coverage properties.

Combining Population and Study Data for Inference on Event Rates