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

Seroprevalence estimates inform uncertainty in epidemic peak and timing. As a natural extension to use of serological data to estimate core epidemiological quantities (11-13) or to map out patterns of outbreak risk (14), the posterior distribution of seroprevalence can be used as an input to any epidemiological model, including a typical SEIR model (3), where the proportion seropositive may correspond to the recovered/immune compartment, or a more complex framework such as an age-structured SEIR model incorporating interventions like closing schools and social distancing (10,15) ( Fig. 1 ; blue annotations). We integrated uncertainty in the posterior estimates of seroprevalence and uncertainty in model dynamics or parameters using Monte Carlo sampling to produce a posterior distribution of trajectories or key epidemiological parameter estimates ( Fig. 1 ; black annotations). Figure 4 illustrates how estimates of the height and timing of peak infections varied under two serological sampling scenarios and two hypothetical social distancing policies for a basic SEIR framework parameterized using seroprevalence data. Uncertainty in seroprevalence estimates propagated through SEIR model outputs in stages: larger sample sizes at a given seroprevalence resulted in a smaller credible interval for the seroprevalence estimate, which improved the precision of estimates of both the height and timing of the epidemic peak. In this case, we assumed the same serological test sensitivity and specificity as before (93% and 97.5%, respectively), but test characteristics also impacted model estimates, with more specific and sensitive tests leading to more precise estimates ( Supplementary Fig. S3 ). Even estimations from a perfect test carried uncertainty, which corresponds to the size of the sample set ( Supplementary Fig. S3 ).