  Globally the SARS-CoV-2 coronavirus has infected more than 59 million people
and killed more than 1.39 million. Designing and monitoring interventions to
slow and stop the spread of the virus require knowledge of how many people have
been and are currently infected, where they live, and how they interact. The
first step is an accurate assessment of the population prevalence of past
infections. There are very few population-representative prevalence studies of
the SARS-CoV-2 coronavirus, and only two American states -- Indiana and
Connecticut -- have reported probability-based sample surveys that characterize
state-wide prevalence of the SARS-CoV-2 coronavirus. One of the difficulties is
the fact that the tests to detect and characterize SARS-CoV-2 coronavirus
antibodies are new, not well characterized, and generally function poorly.
During July, 2020, a survey representing all adults in the State of Ohio in the
United States collected biomarkers and information on protective behavior
related to the SARS-CoV-2 coronavirus. Several features of the survey make it
difficult to estimate past prevalence: 1) a low response rate, 2) very low
number of positive cases, and 3) the fact that multiple, poor quality
serological tests were used to detect SARS-CoV-2 antibodies. We describe a new
Bayesian approach for analyzing the biomarker data that simultaneously
addresses these challenges and characterizes the potential effect of selective
response. The model does not require survey sample weights, accounts for
multiple, imperfect antibody test results, and characterizes uncertainty
related to the sample survey and the multiple, imperfect, potentially
correlated tests.
