Assessing COVID-19 Prevalence in Austria with Infection Surveys and Case Count Data as Auxiliary Information

Countries officially record the number of COVID-19 cases based on medical tests of a subset of the population. These case count data obviously suffer from participation bias, and for prevalence estimation, these data are typically discarded in favour of infection surveys, or possibly also completed with auxiliary information. One exception is the series of infection surveys recorded by the Statistics Austria Federal Institute to study the prevalence of COVID-19 in Austria in April, May and November 2020. In these infection surveys, participants were additionally asked if they were simultaneously recorded as COVID-19 positive in the case count data. In this paper, we analyze the benefits of properly combining the outcomes from the infection survey with the case count data, to analyze the prevalence of COVID-19 in Austria in 2020, from which the case ascertainment rate can be deduced. The results show that our approach leads to a significant efficiency gain. Indeed, considerably smaller infection survey samples suffice to obtain the same level of estimation accuracy. Our estimation method can also handle measurement errors due to the sensitivity and specificity of medical testing devices and to the nonrandom sample weighting scheme of the infection survey. The proposed estimators and associated confidence intervals are implemented in the companion open source R package pempi available on the Comprehensive R Archive Network (CRAN).