  We consider disease outbreak detection settings where the population under
study consists of various subpopulations available for stratified surveillance.
These subpopulations can for example be based on age cohorts, but may also
correspond to other subgroups of the population under study such as
international travellers. Rather than sampling uniformly over the entire
population, one may elevate the effectiveness of the detection methodology by
optimally choosing a subpopulation for sampling. We show (under some
assumptions) the relative sampling efficiency between two subpopulations is
inversely proportional to the ratio of their respective baseline disease risks.
This leads to a considerable potential increase in sampling efficiency when
sampling from the subpopulation with higher baseline disease risk, if the two
subpopulation baseline risks differ strongly. Our mathematical results require
a careful treatment of the power curves of exact binomial tests as a function
of their sample size, which are erratic and non-monotonic due to the
discreteness of the underlying distribution. Subpopulations with comparatively
high baseline disease risk are typically in greater contact with health
professionals, and thus when sampled for surveillance purposes this is
typically motivated merely through a convenience argument. With this study, we
aim to elevate the status of such "convenience surveillance" to optimal
subpopulation surveillance.
