The usefulness of SARS-CoV-2 test positive proportion as a surveillance tool
Authors: Hitchings Matt D.T. , Dean Natalie E. , Garcia-Carreras Bernardo , Hladish Thomas J. , Huang Angkana T. , Yang Bingyi , Cummings Derek A.T. 
Published: July 2020

Comparison of COVID-19 case numbers over time and between locations is complicated by limits to virologic testing confirm SARS-CoV-2 infection, leading to under-reporting of incidence, and by variations in testing capacity between locations and over time. The proportion of tested individuals who have tested positive (test positive proportion, TPP) can potentially be used to qualitatively assess the testing capacity of a location; a high TPP could provide evidence that too few people are tested, leading to more under-reporting.

In this study we propose a simple model for testing in a population experiencing an epidemic of COVID-19, and derive an expression for TPP in terms of well-defined parameters in the model, related to testing and presence of other pathogens causing COVID-19 like symptoms. We use simulations to show situations in which the TPP is higher or lower than we expect based on these parameters, and the effect of testing strategies on the TPP. In our simulations, we find in the absence of dramatic shifts of testing practices in time or between spatial locations, the TPP is positively correlated with the incidence of infection. As a corollary, the TPP can be used to distinguish between a decline in confirmed cases due to decline in incidence (in which case TPP should decline) and a decline in confirmed cases due to testing constraints (in which case TPP should remain constant). We show that the proportion of tested individuals who present COVID-19 like symptoms (test symptomatic proportion, TSP) encodes similar information 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. We conjecture why states may have higher or lower TPP than average. We suggest that collection of symptom status and age/risk category of tested individuals can aid interpretation of changes in TPP and increase the utility of TPP in assessing the state of the pandemic in different locations and times.

Key question: when can we use the proportion of tests that are positive (test positive proportion, TPP) as an indicator of the burden of infection in a state?

If testing strategies are broadly similar between locations and over time, the TPP is positively correlated with incidence rates.

However, changes in testing practices over time and between locations can affect the TPP independently of the number of cases.

More testing of asymptomatic individuals, e.g. through population-level testing, lowers the TPP.

We can identify locations that have a lower or higher TPP than expected, given how many cases they are reporting.

Efficient transmission increases detected cases exponentially, resulting in large changes in confirmed cases compared to factors that change linearly.

Data that could aid interpretability of the TPP include: age of individuals who test positive and negative, and other data on testing performed in high-prevalence settings; and symptom status of tested individuals.