Estimating Seroprevalence of SARS-CoV-2 in Ohio: A Bayesian Multilevel Poststratification Approach with Multiple Diagnostic Tests

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.