  During the COVID-19 pandemic, many institutions such as universities and
workplaces implemented testing regimens with every member of some population
tested longitudinally, and those testing positive isolated for some time.
Although the primary purpose of such regimens was to suppress disease spread by
identifying and isolating infectious individuals, testing results were often
also used to obtain prevalence and incidence estimates. Such estimates are
helpful in risk assessment and institutional planning and various estimation
procedures have been implemented, ranging from simple test-positive rates to
complex dynamical modeling. Unfortunately, the popular test-positive rate is a
biased estimator of prevalence under many seemingly innocuous longitudinal
testing regimens with isolation. We illustrate how such bias arises and
identify conditions under which the test-positive rate is unbiased. Further, we
identify weaker conditions under which prevalence is identifiable and propose a
new estimator of prevalence under longitudinal testing. We evaluate the
proposed estimation procedure via simulation study and illustrate its use on a
dataset derived by anonymizing testing data from The Ohio State University.
