Estimating the proportion of SARS-CoV-2 infections reported through diagnostic testing

The number of positive diagnostic tests for SARS-CoV-2 is a critical metric that is commonly used to assess epidemic severity and the efficacy of current levels of control. However, a proportion of individuals infected with SARS-CoV-2 may never receive a diagnostic test, while many of those who are tested may receive a false negative result. Consequently, cases reported through testing of symptomatic individuals represent only a fraction of the total number of infections, and this proportion is expected to vary depending on changes in natural factors and variability in test-seeking behaviour. Here we combine a number of data sources from England to estimate the proportion of infections that have resulted in a positive diagnosis. Using published estimates of the incubation period distribution and time-dependent test sensitivity, we estimate SARS-CoV-2 incidence from daily reported diagnostic test data. By calibrating this estimate against surveillance data we find that approximately 25\% of infections were consistently reported through diagnostic testing before November 2020. This percentage increased through the final months of 2020, predominantly in regions with a large presence of the the UK variant of concern (VOC), before falling rapidly in the last two weeks of January 2021. These changes are not explained by variation in rates of lateral flow device or PCR testing, but are consistent with there being an increased probability for the VOC that infection will result in an eventual positive diagnosis.