Efficient sampling in disease surveillance through subpopulations: Sampling canaries in the coal mine

We consider outbreak detection settings of endemic diseases where the population consists of subpopulations available for stratified surveillance. Rather than sampling uniformly across the population, one may elevate effectiveness of detection methodology by optimally choosing a sampling subpopulation. We show (under some assumptions) the relative sampling efficiency between two subpopulations is inversely proportional to the ratio of their baseline disease risks. This implies one can increase sampling efficiency by sampling from the subpopulation with higher baseline disease risk. Our results require careful treatment of power curves of exact binomial tests as a function of their sample size, which are non-monotonic due to the underlying discreteness. A case study of COVID-19 cases in the Netherlands illustrates our theoretical findings.