  Governments and public health authorities use seroprevalence studies to guide
responses to the COVID-19 pandemic. Seroprevalence surveys estimate the
proportion of individuals who have detectable SARS-CoV-2 antibodies. However,
serologic assays are prone to misclassification error, and non-probability
sampling may induce selection bias. In this paper, nonparametric and parametric
seroprevalence estimators are considered that address both challenges by
leveraging validation data and assuming equal probabilities of sample inclusion
within covariate-defined strata. Both estimators are shown to be consistent and
asymptotically normal, and consistent variance estimators are derived.
Simulation studies are presented comparing the estimators over a range of
scenarios. The methods are used to estimate SARS-CoV-2 seroprevalence in New
York City, Belgium, and North Carolina.
