Accounting for incomplete testing in the estimation of epidemic parameters

As the COVID-19 pandemic evolves across the world and the United States, it is important to understand its evolution in real time and at regional levels. The field of infectious diseases epidemiology has highly developed modeling and estimation strategies that yield relevant estimates. These include the doubling time of the epidemic, i.e., the number of days until the number of cases doubles, and various representations of the number of cases over time, including the epidemic curve and associated cumulative incidence curve. While these quantities are immediately estimable given current data, they suffer from dependence on the underlying testing strategies within communities. Specifically, they are inextricably tied to the likelihood that an infected individual is tested and identified as a case. We clarify the functional relationship between testing and the epidemic parameters of interest, and thereby demonstrate simply sensitivity analyses that explore the range of possible truths under various testing scenarios. We demonstrate that crude estimates that assume stable testing or complete testing can be overly-optimistic.