Estimating SARS-CoV-2 seroprevalence and epidemiological parameters with uncertainty from serological surveys

Daniel B Larremore; Bailey K Fosdick; Kate M Bubar; Sam Zhang; Stephen M Kissler; C. Jessica E. Metcalf; Caroline Buckee; Yonatan Grad

Three sources of uncertainty complicate efforts to learn population seroprevalence from subsampling. First, tests may have imperfect sensitivity and specificity; estimates for COVID-19 tests on the market as of April 2020 reported specificity between 95% and 100% and sensitivity between 62% and 97% (Supplementary Table S1 ). Second, the population sampled will likely not be a representative random sample, particularly in the first rounds of testing, when there is urgency to test using convenience samples and potentially limited serological testing capacity. 3 Test sensitivity/specificity, sampling bias, and true seroprevalence influence the accuracy and robustness of estimates. To integrate uncertainty arising from test sensitivity and specificity, we produced a Bayesian posterior distribution of seroprevalence that accommodates uncertainty associated with a finite sample size ( Fig. 1; green annotations) . We denote the posterior probability that the true population serology is equal to θ, given test outcome data X and test sensitivity and specificity characteristics, as Pr(θ | X). Because sample size and outcomes are included in X, and because test sensitivity and specificity are included in the calculations, this posterior distribution over θ appropriately handles uncertainty (see Methods).