Discriminative Bayesian Serology: Counting Without Cutoffs

During the emergence of a pandemic, we need to estimate the prevalence of a disease using serological assays whose characterization is incomplete, relying on limited validation data. This introduces uncertainty for which we need to account. In our treatment, the data take the form of continuous assay measurements of antibody response to antigens (eg. ELISA), and fall into two groups. The training data includes the confirmed positive or negative infection status for each sample. The population data includes only the assay measurements, and is assumed to be a random sample from the population from which we estimate the seroprevalence. We use the training data to model the relationship between assay values and infection status, capturing both individual-level uncertainty in infection status, as well as uncertainty due to limited training data. We then estimate the posterior distribution over population prevalence, additionally capturing uncertainty due to finite samples. Finally, we introduce a means to pool information over successive time points, using a Gaussian process, which dramatically reduces the variance of our estimates. The methodological approach we here describe was developed to support the longitudinal characterization of the seroprevalence of COVID-19 in Stockholm, Sweden.