Estimating the cumulative rate of SARS-CoV-2 infection

Accurate estimates of the cumulative incidence of SARS-CoV-2 infection remain elusive. Among the reasons for this are that tests for the virus are not randomly administered, and that the most commonly used tests can yield a substantial fraction of false negatives. In this article, we propose a simple and easy-to-use Bayesian model to estimate the infection rate, which is only partially identified. The model is based on the mapping from the fraction of positive test results to the cumulative infection rate, which depends on two unknown quantities: the probability of a false negative test result and a measure of testing bias towards the infected population. Accumulating evidence about SARS-CoV-2 can be incorporated into the model, which will lead to more precise inference about the infection rate.