A Framework for SARS-CoV-2 Testing on a Large University Campus: Statistical Considerations

We consider testing strategies for active SARS-CoV-2 infection for a large university community population, which we define. Components of such a strategy include individuals tested because they self-select or are recommended for testing by a health care provider for their own health care; individuals tested because they belong to a high-risk group where testing serves to disrupt transmission; and, finally, individuals randomly selected for testing from the university community population as part of a proactive community testing, or surveillance, program. The proactive community testing program is predicated on a mobile device application that asks individuals to self-monitor COVID-like symptoms daily. The goals of this report are (i) to provide a framework for estimating prevalence of SARS-CoV-2 infection in the university community wherein proactive community testing is a major component of the overall strategy, (ii) to address the issue of how many tests should be performed as part of the proactive community testing program, and (iii) to consider how effective proactive community testing will be for purposes of detection of new disease clusters. We argue that a comprehensive prevalence estimate informed by all testing done of the university community is a good metric to obtain a global picture of campus SARS-CoV-2 infection rates at a particular point in time and to monitor the dynamics of infection over time, for example, estimating the population-level reproductive number, R0). Importantly, the prevalence metric can be useful to campus leadership for decision making. One example involves comparing campus prevalence to that in the broader off-campus community. We also show that under some reasonable assumptions, we can obtain valid statements about the comprehensive prevalence by only testing symptomatic persons in the proactive community testing component. The number of tests performed for individual-level and high-risk group-level needs will depend on the disease dynamics, individual needs, and testing availability. For purposes of this report, we assume that, for these groups of individuals, inferential precision --- that is, the accuracy with which we can estimate the true prevalence from testing a random sample of individuals --- does not drive decisions on the number of tests. On the other hand, for proactive community testing, the desired level of inferential precision {in a fixed period of time can be used to justify the number of tests to perform {in that period. For example, our results show that, if we establish a goal of ruling out with 98\% confidence a background prevalence of 2\% {in a given week, and the actual prevalence is 1\% among those eligible for proactive community testing, we would need to test 835 randomly-selected symptomatics (i.e., those presenting with COVID-like symptoms) per week via the proactive community testing program in a campus of 80k individuals. In addition to justifying decisions about the number of tests to perform, inferential precision can formalize the intuition that testing of symptomatic individuals should be prioritized over testing asymptomatic individuals in the proactive community testing program.