Abstract
Comparison of coronavirus disease 2019 (COVID-19) case numbers over time and between locations is complicated by limits to virological testing to confirm severe acute respiratory syndrome coronavirus 2 infection. The proportion of tested individuals who have tested positive (test-positive proportion, TPP) can potentially be used to inform trends in incidence. We propose a model for testing in a population experiencing an epidemic of COVID-19 and derive an expression for TPP in terms of well-defined parameters related to testing and presence of other pathogens causing COVID-19-like symptoms. In the absence of dramatic shifts of testing practices in time or between locations, the TPP is positively correlated with the incidence of infection. We show that the proportion of tested individuals who present COVID-19-like symptoms encodes information similar to the TPP but has different relationships with the testing parameters, and can thus provide additional information regarding dynamic changes in TPP and incidence. Finally, we compare data on confirmed cases and TPP from US states up to October 2020. We conjecture why states might have higher or lower TPP than average. Collection of symptom status and age/risk category of tested individuals can increase the utility of TPP in assessing the state of the pandemic in different locations and times.